Audio problem: When Wesley first walks into the textile factory and sees Sloane talking to a worker, the first shot of Sloane shows his mouth moving and you hear him talking. In the very next close up shot of Sloane, you still hear his voice, but his lips aren't moving. He just turns his head towards the worker, then away.
Continuity mistake: In the scene where the Corvette goes head to head with Wesley's Mustang to flip over the limo and kill the target, while the Mustang flips in the middle of the air, it's going clockwise. But in the landing scene right after, it lands in a counter-clockwise movement. We actually see it landing while spinning clockwise, but the camera is now behind the car, which should reverse the way we see it spinning. For example, if you upturn a bicycle and spin its wheel clockwise, if you move around to the other side of the bike, it will now, from your new perspective, be spinning counter-clockwise. It's difficult to see as it happens very, very quickly, but it is very much noticeable that it lands while spinning in the opposite direction.
Plot hole: Just after the shootout in the grocery store, Wesley's dad nearly runs him over in the pet truck. Before this, it seemed as though he may have wanted to kill him, but he just hadn't gotten a clear shot. It's highly doubtful that he would have trusted Fox, his enemy, to swipe Wesley into the car literally one second before he would have been plowed by the truck. Being the best assassin in the entire Brotherhood, there's no reason to think that he could act careless at a time like this, especially when doing so could easily cost the life of his son.
Continuity mistake: When Wesley slices the Butcher's neck, the far angle shows that he cuts him on the left. But when the close-up comes, it's on the right side of the neck. And when Fox is beating Wesley up, as she punches him, the close-up of the brass knuckles shows them on her left hand when the wide scene showed the brass knuckles on her right hand.
Continuity mistake: After Wesley kisses Fox in his old apartment and sees his father and the bullets collide, Wesley chases his father up some stairs and starts shooting at his father/the screen with his left wrist under his right firing hand. When it shows him from behind he is holding the gun with two hands. When you see him from the front again he is holding the gun right over left hand again.
Continuity mistake: In the scene where Wesley is chasing Cross on the train through the tunnels, where the back of the train falls off the bridge; the last car is shown exiting the tunnel, and about four seconds later, begins to slide off the track and pulls the second car with it. They cut back inside the train to show you people falling and screaming, and the next shot on the exterior of the train, you can see the last car is exiting the tunnel again, and the two cars ahead of it have fallen off and are what's beginning to pull the train off.