Continuity mistake: Season 2, Episode 5: "Goodbye to All That" - We see Marty Bedell playing on his Xbox 360 with a headset attached to his right ear. But when the T-888 arrives at his house to kill him and he goes to answer the door, the headset is gone. There was absolutely no time for Marty to remove the headset as the camera cuts too quickly.
Continuity mistake: When John and Pyle are at the shooting range, John's protective glasses are up on his head when he fixes Pyle's gun, down on his face when he fires the gun, back up on his head after firing and then back down on his face when he gives the gun back to Pyle. They're then back on his head before taking them off before the scene ends.
Other mistake: When Sarah puts Marty on the bus on his way home he steps onto the first step and turns to face Sarah as the door closes and the bus departs. It is against the law in California for buses to begin moving until passengers are on the main deck of the bus (one step up from the boy). This law was enacted after a child fell from the entry step of the bus (exactly where Marty stood), the doors opened and they were run over by the bus. California operates a zero tolerance policy on this matter; drivers know that a single infraction will result in the loss of their commercial drivers license and is taken very seriously by all drivers, without a single infraction having been reported in years.