Continuity mistake: This basically happens in nearly every episode. Whenever Michael's mom is smoking, which she does a lot, her cigarette and smoke change size and position with every shot. Although it's hard to keep a cigarette burning the same way with each take, it seems as if no attempt was made at all.
Factual error: When Michael attempts to start the Charger, the starter just clicks, indicative of a dead battery or faulty starter. He checks his father's logbook and reads "spark plugs." Unless the cylinders are filled with an non-compressible liquid, there is no way that spark plugs are going to prevent the engine from cranking.
Continuity mistake: Michael has to prove himself for his new "boss" Concha Ramirez. He walks across the street to Fiona and starts a mock robbery to get her purse. When he approaches the car, the window is down. Three seconds later he is at the car and the window is up so Michael can break it. Watch as the window frame goes from clean (as if the window were down) to broken pieces of glass on the frame between shots.
Continuity mistake: Michael is having a meeting with the guy who is asking how Michael found out about him (where Sam is standing guard with the sniper rifle.) Michael has a gun pulled on him and is trying to escape. As Michael is trying to leave in the Charger, he pulls backwards and makes a 90 degree turn so that the passenger side of the Charger is facing the guy with the gun. The windshield could not have been shot from this angle. The next camera shot Michael is driving backwards again with the windshield facing the guy so he can shoot a hole in the center of Michael's windshield.
Continuity mistake: When the heroin importer is questioning Sam, he has his hand around his face, with his fingers touching his ear. When the shot moves to the front, his hand is more on his throat and nowhere near his ear. When we cut to the back, his hand moves again.
Continuity mistake: When Michael is on the phone with the heroin dealer at the docks, he has his phone at his left ear. When the camera moves to a shot from the back, there's no phone near his face (or in the frame for that matter) and his mouth doesn't move while talking. When the shot cuts back, the phone instantly is back at his ear.