Forgeries of the stamps themselves were crudely produced for the penny packet trade. They resemble the genuine stamps only approximately and should fool no one who takes the time to compare them closely, although very badly printed originals (in particular, plate II 2 reales) can look "wrong" until they become familiar.
Reprints were made later (possibly during the 1880s) from original plates. Conventional wisdom has it that only the four and eight reales were sufficiently valuable to be worth the trouble involved, and these mostly imitate the rare districts, for the same reason. According to the Follansbee catalogue, the paper used was more opaque than any of the original papers. (It also seems to be smoother in texture). Victoria Benozio adds that, if suspected stamps are placed face-down, originals will show the designs faintly, while reprints will not. These will usually have forged district handstamps and forged cancellations applied as well, both of which are points of comparison / recognition. Many of these typically have both the district overprint and cancellation applied in exactly the same greyish ink and the colors the forgers used tends to be the same for all copies printed. Remainders, being genuine printings on genuine paper, are probably only recognizable by discrepancies between original and forged district overprints and cancellations (assuming the forgers didn't give these impossible dates). In practice, the more common material tends to pass without question, it being thought that the forgers ignored districts like Mexico, Veracruz etc., concentrating on imitating sought-after rarities.
Forged overprints are often found on reprints, but could be found on genuine stamps, too. The more rare overprints should be expertized, since the detection of a forgery often requires comparison to a known genuine copy, and perhaps some experience.
Forged cancellations are really beyond the scope of this site, but they do occur. They are most often found on forged stamps, reprints and stamps with rare and forged overprints.
The best place to start looking for information about the stamps of Mexico is the MEPSI website at http://www.mepsi.org