The black man is hit in the back with an axe, wounding him. After that, Jason forces the axe straight throught the man's body, killing him. Later on, we see the man lying facedown in water, with the axe in his back again.
Clay can be seen briefly in a few scenes with a fixed blade knife in a sheath on his belt. Not only does he never think to use it to defend himself against Jason, he looks franticly for other weapons in the barn right before Jason crashes threw the window behind him. Did he forget that he had the knife?
When Clay walks out of the house toward his motorcycle carrying his backpack, it switches from one shoulder to the other, as well as being carried in his hand by its traps, in each different camera angle.
After the verbal altercation with Trent at the lake house, Jenna leaves with Clay Miller, who is carrying a satchel. As they approach Miller's motorcycle, notice how the position of the satchel changes from being strapped around Miller's left shoulder, to being carried in his right hand, and, finally, back to his left shoulder.
When Trent and Bree are having sex in the bedroom. Bree is seen sitting up with her hands on top of her head holding her hair. When it cuts to showing Trent's upper body half. You can see Bree's hands by his neck and shoulders. When it cuts back to the same side view as before with Bree sitting on top of Trent as he is laying down. Her hands are all of a sudden back at the top of her head holding her hair. As quick as the shots are shown there is clearly no time for here to get her hands back up that fast.
Chelsea gets hit by the boat after falling off the wake board, and when she emerges from the water, we see her holding her head as there is blood from her head. When she hides under the boat pier whilst Jason is on top of it looking for her, the blood is gone and there is no visible injury
Clay puts one of his missing persons poster on the back of the Escalade and there's a close up shot of the poster as the vehicle drives away from the outpost store. The ensuing shot is of the vehicle entering the city limits of Crystal Lake, passing by the sign, however there's no poster on the back of the vehicle.
In the scene where Lawrence gets killed with the ax there is no mistake. Jason throws a double sided ax into Larry's back. Larry falls forward onto logs screaming. Jason then comes behind Larry turning him over and stomping on his body once. this causes one side of the ax to come through his chest. The other side of the ax is still in his back and was never removed. That was the last we see of Larry.
When Chelsea is wake boarding, when she first gets up, she is clearly putting her left foot forward (regular stance) however the first shot immediately after this, her right foot is forward (goofy), yet every other shot she is wake boarding with her left foot forward (regular).
In the scene where Jason is walking up to the house and sees Trent and Bree having sex through the bedroom window, you can clearly see the ceiling fan above them is on and spinning. In the next scene which is a close up of Bree from the waist up, the ceiling fan is not moving at all.
In final scene Jason's mask strap is ripped hanging off of the mask. Then it is reattached when he comes out of water. But him returning may have been a dream of the final characters. In that case then his mask could be in any condition.
The goof items below may give away important plot points.
When Jason throws Bree out of the house onto the police car, the windshield breaks like house glass. Modern windshields are generally made of laminated safety glass, a type of treated glass, which consists of two curved sheets of glass with a plastic layer laminated between them for safety, and don't shatter so much as crumble.
When Chewie gets stabbed right under his chin, the position of the screwdriver changes from dead center to far right (away from the camera) so much that you clearly see it's too far over to actually be in him, more like it's on the outside of his neck.