Continuity mistake: When Jax and his crew meet up with a Hispanic gang to sell them guns and are outnumbered, they run in the station wagon. The run the station wagon through a gate and roll it, destroying the front end, but magically the station wagon's front end appears with little damage afterwards.
Other mistake: Abel was 18 months old when Thomas was born. All through the series, Thomas hardly ages. In season 7 Abel is 5 and in kindergarten yet Thomas looks younger than 3. He's not even walking or talking yet! Thomas should be at least 3 years old according to the time span of the series.
Plot hole: When the guys break into the safe house and free the witness against Bobby, they are wearing masks to hide their identities. Yet after freeing the witness, Jax and Tig decide to get involved in a fist fight inside the house which would leave their DNA all over the place. Since both are undoubtedly on the police database, it would take no time at all for the police to find at least two of the culprits who assaulted two officers, an ATF agent and intimidated their star witness.
Character mistake: Tig gets bit on the right butt cheek. Tara tells Chibs to give him a local, which is a numbing injection so she can stitch him up. Problem is that Chibs does the injection in the left butt cheek. You are supposed to give the injection close to the wound to numb it before stitches.
Deliberate mistake: When Tara is talking to Gemma in the parking lot of Stockton Prison, the chrome bumper of Tara's SUV is blurred out, probably to cover up visible crew and equipment. It look unnatural, since the image is sharp enough that you can see the radiator itself behind the grille, and the numberplate is perfectly sharp.