Continuity mistake: When the T-1000 walks past the deactivated T-800 just after being shot at by Kyle Reese, you can see that the T-800 has taken a lot of damage to the face and the nose is missing. Once the T-800 gets up after being reactivated you can see that the nose is back with a lot less damage to the face with a close up shot.
Factual error: During the opening narration Kyle Reese states that Skynet attacks humanity on August 12, 1997. In the shot of missiles decimating San Francisco, multiple 2005-present Toyota Priuses, Dodge Chargers and other late model cars are seen.
Continuity mistake: In the bus scene on the Golden Gate bridge, right after the bus flips end-over-end, we see it sliding broadside from Pops' point of view through the hole in the police car windshield, at most a few hundred feet ahead. At this point, the bus falls over the side of the bridge, breaks apart, then catches and hangs there. In the ensuing wide angle shot, even though Pops was a mere block away and racing at top speed, his car is nowhere in sight. What's taking him so long? Did he take the scenic route? Perhaps stop for beverages? Meanwhile, as Kyle and Sara snap out of it, exchange some dialogue, and begin scrambling upward to safety with John Connor again in hot pursuit, a full minute passes before Pops finally rolls in to save the day. (01:28:35 - 01:29:15)
Continuity mistake: After the truck crashes into the fire hydrant, Kyle picks up the gun and searches the back to shoot Pops. He appears around the back and aims the gun, with the gun raised to his chin. The shot then cuts to a closer shot of Kyle, with the gun now suddenly lowered to his chest. (00:28:50)
Factual error: Both Kyle and Sarah show no signs of injury after they have been hit by the car in 2017 when they appear on the freeway, despite being thrown from the bonnet and landing naked in the road.
Visible crew/equipment: When Miles Dyson, president of Cyberdyne, is talking to Danny Dyson and John Connor; whilst they are all looking towards the production line of liquid metal, you can see that the bodypack transmitter falls/dangles off under Miles Dyson's suit jacket. And as he steps off the shot, you can see him reach under with his hand to attempt to hide it.
Continuity mistake: After Pops puts the deactivated T-101 in the truck, the mouth is closed in typical grim determination type look. A few minutes later, the expression has changed somewhat and the mouth is slightly agape. Later, in the factory, the 101 is laid on the floor, and the face is in the original position of determination.
Continuity mistake: John has the scars on his face from Terminator Salvation events indicating that it's the same and original timeline, and also Skynet was going to send the T-800 to 1984, but the original T-800 is sent once again in Genisys.