Factual error: Grissom sees an information card for a 17th century suit of Japanese armour (just the card, not the suit itself), and immediately deduces that the suit must actually be from the 19th century, because the Japanese military was formed in the 1860s. That military was westernised, and did not wear armour. There was nothing on the card that falsely referred to that military as being established earlier, or indicated that the suit belonged to it. There was a reference to the "military class", but that was historically correct, and meant the Samurai.
Factual error: They talk about the type of tubes used in HIV tests. There are no special tubes specific for HIV testing alone. It is one generic tube that can be used for a multitude of tests including HIV. It did not seem as though Greg knew that she had gone for HIV testing before he ran the tests, so he should not have concluded that it was the type of tube used for HIV testing, only Catherine or Warrick should have made that connection.