The Shock of the New (1) - S1-E1
Continuity mistake: Towards the end of this episode, Emma tells Brennan that her powers don't work if she's stressed. The first time they met, earlier in this episode, she is running from the GS agents and very panicked and stressed, yet she easily uses her powers to ask for his help.
Crime of the New Century - S1-E9
Continuity mistake: In the fight scene at the start of the episode, Jesse knocks one of the GS agents into the water - in subsequent shots he has disappeared.
Continuity mistake: When Andrea jumps off the roof at the end of "Where Evil Dwells", season 3, she is falling face down for the first two shots, then when it switches to a third shot she is falling face up.