a) never erred even in non-Torah matters
b) never erred in Torah matters, but might rarely have erred in science
c) never erred in Torah matters, but relied on the faulty science of their time
d) definitely had faulty science and possibly erred in some history as well
e) did pretty well but made a lot of mistakes
f) Leave this question out of my results
For me, at least, this question overlaps with the last, though it is not the same.
I will first discuss whether Chazal "erred in Torah matters." If this question is asking whether there are halachic or hashkafic statements in the Talmud that are based on incorrect recollection, misunderstanding, or faulty reasoning, I think the answer is clearly that there are. Why else would Rav Dimi and Ravin, for example, argue all the time about what Rabbi Yochanan said? How could anybody ever question anybody else's kal vachomer? How could Rabbi Yehudah ben Tabbai have wrongly ordered someone executed without having adhered to the proper judicial procedures (Makkot 5b)? How could Rabbi Yehoshua et al. have been contradicted by a heavenly voice in their famous dispute with Rabbi Eliezer? In the absence of evidence that the Talmudic sages had perfect memories or flawless analytical minds, I do not believe they had either.
The fact that Chazal were imperfect human beings, just like the rest of us, does not, however, diminish the halachic and hashkafic authority of the Talmud. Even though any given halachic pronouncement of the Talmud may be based on flawed information or skill, it is still binding. Torah lo bashamayim hi; our obligations in the service of God are determined by the earthly, human, halachic process, part of which, in our day and age, is the supremity of the Talmud. Our job as Jews is, ultimately, to do what God expects of us, and God expects us to follow the Talmud, even if he "personally" thinks the Talmud said something stupid.
Mistakes in science? I opined on this topic in the last post on the Orthodoxy Test (#15). Just to summarize in one sentence: I haven't come across sufficient evidence to dissuade me from my initial, intuitive assumptions that (1) Chazal, like all other people, weren't omniscient, in science or in anything else; and (2) some of their scientific beliefs - like the shape of the Earth, or their model of the solar system, or the manner in which lice are formed - are wrong. (I suppose (2) is not really an intuitive belief, but it is one in which I have a great deal of confidence.)
Mistakes in history? The issue that comes immediately to mind is the dating of the construction of the Second Temple: modern archaeology claims it to have been built 166 years (if memory serves) before the Talmud says it was. Could Chazal have been wrong about this, or about other historical assertions that they made? Why not? Again, where's the proof they had perfect memories, never garbled their information, and kept flawless records of every single fact and event?
I chose (d). (E) sounds to me to be suggesting that Chazal's words are not binding, because their judgment was flawed, and if we can judge better, we can override what they said. This assertion is false, because it does not take into account the halachic process and the authority it has lent to the Talmud, as discussed above.