When Tony and the campers are going on their hike as punishment for not losing weight, Tony incorrectly talks about the Greek legend of Icarus who was sentenced to push a boulder up a hill for all eternity. Icarus is a Greek legend known for flying too close to the sun. It was Sisyphus to whom Tony should have been referring.
The position of one of the campers that Lars pushes into the water before running over to Julie; when the camper is pushed, he tips over, but in the next shot, he can be seen falling upright into the water.
When the boys are playing softball against Camp MVP, Jerry swings and misses and his bat flies directly over Tim's head and hits the fence. In the next shot, the bat hits Kenny the Cameraman, who was nowhere near the bench in the previous shot.
In the main dorm, there is a bathroom door that says "girls". Which is fine, but the camp is an all boys campus. However, this may not be a goof - it could be rented as a girl's camp at other points in the summer.
Tony offers Nicholas a "chocolate kiss" to lure him closer to his cage. The boys had only just been through their all-night food and candy orgy. It's highly unlikely that Nicholas would be tempted by a little piece of chocolate, given he's been able to have whatever he wants to eat for days now.
During the dance with the girls camp, Jerry is seen wearing a sports coat and multicolor tie, and Nicholas is wearing a Les Miserables t-shirt. When Tony breaks up the dance he tells the staff to put the food away, and by the tables there are 2 boys wearing the same exact outfits that Jerry & Nicholas were wearing before.