What makes the information contained in the artwork of Ancient Rome--Roman Republic to Roman Empire--reliable and/or not reliable?
Since you have been asking questions regarding fashion and clothing, I will answer this question with reference to that area.
The main thing that makes art work from ancient Rome reliable is that it was produced by people who would have had firsthand knowledge of what people in Ancient Rome were wearing. This was not artwork that was produced centuries after the fact. Since it is typically depicting contemporary subjects, it should be generally reliable.
The main thing that would make this kind of artwork unreliable is that it was not necessarily produced for the purpose of documenting fashion. Much of the art that was produced in ancient Rome was produced for the pleasure of rich patrons of the arts. Artists might, therefore, have produced art that would have appealed to those rich people, not art that documented how things really were. For example, if an artist happened to paint a scene that had slaves in it, he might not want to portray the slaves looking wretched since that might detract from the patron’s enjoyment of the painting. Thus, the fact that this art was not produced for documentary purposes might make it less reliable.