Summary of problems:
Explore Evolution equates alleged controversy about evolution with controversies over plate tectonics, climate change, and string theory. This elevates social and political controversies to the same level as scientific controversy. Whether evolution takes place and explains the diversity of life is no longer scientifically controversial; the remaining controversy derives from political and cultural concerns.
String theory is currently scientifically controversial, just as plate tectonics was controversial until the 1960s, and global warming was scientifically controversial until the late 1990s. Evolution was last scientifically controversial in the 19th century and that controversy ended by the 1870s. By that date, essentially all practicing scientists accepted that natural causes could account for the formation of new species and that all living things share a common ancestry.
Full discussion:
Explore Evolution describes these supposed controversies in this passage from the Preface:
Controversies in science are nothing new. As recently as the early 1960s, for example, most geologists accepted the geosynclinal theory as the explanation of how mountain ranges form. After a significant period of controversy, most scientists came to accept the theory of plate tectonics because it provided a better explanation for a larger number of scientific observations. Yet without understanding the arguments that led to the acceptance of plate tectonics, it is very difficult to understand the theory itself or its current standing in the scientific community.
Today we continue to have important unresolved scientific controversies in many branches of science. In climatology, for example, scientists disagree over what global warming is, whether it is a natural phenomenon or a man-made problem, how big a problem it presents, and what (if anything) should be done about it. In theoretical physics, scientists disagree over the meaning and importance of string theory.Explore Evolution, p. vi
This passage conflates scientific controversies with social controversies, an error that runs throughout Explore Evolution. In general, theories are scientifically controversial until they can provide testable and well-tested explanations for phenomena. By that standard, string theory is currently controversial, but global warming and plate tectonics are not scientifically controversial today. Despite the cessation of scientific controversy over evolution or global warming, both concepts continue to generate social controversy over their implications for policy or for personally-held religious views.
String theory provides a powerful theoretical model for unifying our understanding of various physical forces. On the other hand, it has yet to yield testable predictions that can be measured on current equipment in a way that distinguishes them from results generated using the existing 'standard' theory (see Smolin [2006], The Trouble with Physics, for an excellent review of these problems). It is therefore unknown whether the novel aspects of string theory are correct. String theory may be right; it may be a dead end; science simply does not know yet. Improvements in our scientific instruments may someday allow physicists to validate or disprove string theory. At that time, some or most of the controversy over its validity will die down and physicists will shift to debates over details of string theory rather than to debates over its scientific status per se. 
Pangaea and Fossil Distribution: from United States Geological Survey
This scientific process for examining ideas was used for the now-accepted explanations plate tectonics, evolution, and global warming. When Alfred Wegener proposed that the seeming lock and key fit of the coastlines of South America and Africa could be explained by moving continents, he backed his proposal with significant paleontological evidence, but could not explain the mechanisms involved in continental movement. Later research showed evidence of new crust forming as molten rock rose from deep sea rifts, including one midway between the African and South American coasts. Geologists developed a model in which plates are pushed together and pulled apart, creating new crust and destroying old crust, and found that it explained not only the evidence Wegener provided, but other questions about the formation of mountain ranges and the occurrences of volcanoes and large earthquakes.
Once Wegener s idea had a testable model and a literal mountain of supporting evidence, it was rapidly accepted by geologists and ceased to be controversial. It should be noted that, contrary to Explore Evolution s claim, students have no trouble understanding plate tectonics without first learning about discredited ideas that preceded it.
In fact, a similar process took place in the 19th and early 20th centuries as scientists addressed Darwin and Wallace s evolutionary ideas. The idea of common ancestry of living things was rather quickly accepted in the scientific community; Darwin's choice for the most important mechanism of evolution, natural selection, was slower to be accepted. A major problem was the lack of a mechanism for new variation to be replenished each generation after natural selection had whittled out the survivors, a problem that could be solved only with a clearer understanding of how characteristics were passed down from generation to generation. Critics rightly objected to the model of inheritance Darwin proposed in the Origin of Species, which involved simply averaging parental characteristics. Of course, none of Darwin's contemporaries understood how heredity worked either: it wasn't until the rediscovery of Mendelian genetics in the early 20th century that an accurate basis for inheritance became available.
Mendelian genetics resolved a key scientific controversy that surrounded natural selection, much as sea-floor spreading resolved a key scientific controversy about continental drift. As scientists integrated their new understanding of genetics with the existing evolutionary ideas, they produced a more comprehensive picture of evolutionary biology, often referred to as the Modern Synthesis. But during the debate about the validity of natural selection and the development of the Modern Synthesis, scientists were not seriously questioning whether evolution occurred or whether universal common descent was the most reasonable inference from the data. Those scientific questions had been resolved decades earlier.
More recently, climate scientists went through a similar transition regarding global climate change. The idea that adding carbon dioxide to the atmosphere might cause global warming was first proposed in 1896 by Svante Arrhenius. Until modern supercomputers, it was impossible to fully model the global climate or to predict the consequences of human interactions with the atmosphere. Without modern satellites and high-altitude measurements, it was impossible to test those models. When weather stations demonstrated a global trend of rising temperatures in the 1980s and 1990s, some scientists attributed that change to the rise in atmospheric carbon dioxide measured globally, while others felt that the models available at the time were not accurate enough, and that the natural variability of the climate was too large relative to measured temperature changes to require anything but a natural explanation. In 1990, scientists with the non-partisan Intergovernmental Panel on Climate Change (IPCC) agreed that there is a natural greenhouse effect, that emissions resulting from human activities are substantially increasing the atmospheric concentrations of the greenhouse gases. At the time, they concluded that global mean surface air temperature has increased by 0.3 to 0.6 C over the last 100 years. The size of this warming is broadly consistent with predictions of climate models, but it is also of the same magnitude as natural climate variability. Thus the observed increase could be largely due to this natural variability; alternatively this variability and other human factors could have offset a still larger human-induced greenhouse warming. The unequivocal detection of the enhanced greenhouse effect is not likely for a decade or more.
However, by 1995, the IPCC report found that The balance of evidence suggests a discernible human influence on global climate, observing that [s]ince the 1990 IPCC Report, considerable progress has been made in attempts to distinguish between natural and anthropogenic influences on climate. In 2001, the IPCC's Third Assessment Report found There is new and stronger evidence that most of the warming observed over the last 50 years is attributable to human activities, and concluded that most of the observed warming over the last 50 years is likely to have been due to the increase in greenhouse gas concentrations. In IPCC reports, likely means that the scientists assess the likelihood of the statement being true at between 66-90% chance, while the 1995 statement about the balance of evidence refers to a chance slightly higher than 50%. When the IPCC released its Fourth Assessment Report in 2007, the team of climate scientists concluded that [w]arming of the climate system is unequivocal, and that [m]ost of the observed increase in globally averaged temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations." Very likely means better than 90% chance.
Between the third and fourth reports, a researcher on the sociology of science demonstrated the growth of a scientific consensus behind anthropogenic climate change. Dr. Naomi Oreskes published a paper in the December 3, 2004 issue of Science surveying publications about climate change between 1993 and 2003. Oreskes classified those papers as either accepting the 2001 consensus that most of the observed warming over the last 50 years is likely to have been due to the increase in greenhouse gas concentrations," rejecting that statement, or taking no position on it. Of 928 papers identified in scientific databases which contained the phrase global climate change, 75% supported the IPCC consensus, 25% did not discuss it, and none explicitly rejected it. While such papers may exist, it is clear that there was not a vociferous debate between scientists in the field over whether humans are causing global warming. That consensus can also be demonstrated by statements from major scientific bodies, including the National Academies of Science, the American Meteorological Society, the American Geophysical Union, and the American Association for the Advancement of Science, all essentially restating the IPCC assessment.
This is not to say that debate in any of these fields has ended. Just as geologists continue to make new discoveries about plate tectonics, and to debate those discoveries with intensity, evolutionary biologists continue to debate the relative influence of the various forces driving evolution, and climate scientists continue to disagree about the precise implications of current human activities for the future of Earth's climate. The era of controversy ends when the scientific community comes to accept that a particular theory is testable and offers superior explanations for known phenomena.
The era of controversy ended for evolution decades ago, and Explore Evolution's claims to the contrary are disingenuous. The current controversy surrounding evolution is not a scientific controversy. The comparison to global warming is instructive. Global warming is scientifically uncontroversial, but the question of whether society ought to make some effort to avert it, and what should be done in that event, are subject to intense disagreement. Thus, global warming is scientifically uncontroversial, but generates controversy because of its policy implications. Similarly, evolution is not scientifically controversial, but does generate social controversy because of people's disagreements about its philosophical, religious and metaphysical implications. Those controversies cannot be resolved based on empirical scientific evidence alone.