In many episodes, the team are examining hazardous, unknown substances. They invariably do so without any form of protective clothing or protocol.
In season 3, 11th episode 26th minute (Reciprocity) Walter said that his blood type is A+, but in the "Welcome to Westfield" S4E12-15:00, his blood type was O- so he could donate.
Whenever a shapeshifter is wounded they are shown to bleed "mercury." However, mercury is not sticky. It would not be stuck to the bodies or clothing around the wounds, nor stain the gloves of the investigators. It would simply spill onto the ground. This is not actually a goof, because what they bleed isn't entirely mercury, it's a weird mix of blood and mercury.
Most shots of "Harvard" are actually Yale Univ. Mostly cross campus courtyard and Old campus courtyard.
Beginning in season one, establishing shots show the teams headquarters to be in a skyscraper which title cards identify as the "Boston Federal Building." However the building shown is actually Hancock Tower, a privately owned office building which is one of the most recognizable landmarks in Boston. The FBI is located in One Center Plaza which is across the street from Homeland Security office located in the John F. Kennedy Federal Building located downtown at Government Center. Both buildings are in direct proximity to Boston City Hall, a city courthouse, police station, local NBC/CW television station and immigration offices.
Despite being set in Boston many of the neighborhoods bear no resemblance to the actual Boston neighborhoods they are supposed to represent.