Continuity mistake: When Adam is in the park watching for roller bladers to miss the turn and crash, he places a stick in the path and the 3rd skater trips on it. When the skater falls, he ends up in the water and after he strikes the water you can see that the large flat rock on his left begins to move and bob around in the wake of the water.
Revealing mistake: When Sandler is talking to the kid, they are passing through the Greenwich Village area. In the next shot, they are walking in front of a "clock building" (one side has the numbers 1-12 and 0-59). This building is located on John Street in the financial district, which is over 2 miles away.
Continuity mistake: When Sonny, Julian, and the two gay guys are in the park eating, the gay guy on the left (in the grey sweatshirt) is holding a bag of potato chips in his lap. First you can see the front of the bag, then the camera cuts to another shot, and when it returns, the back of the bag shows. This occurs many times in this scene.
Audio problem: At the park, when Sonny is talking to his two friends, Julian throws a stick in the path of a rollerblader. The scene closes with a laughing Julian proud of the fact that he tripped the poor rollerblader. We hear the blader (off-screen) yell out "G**d**n stick!" This is clearly Adam Sandler's voice (most likely dubbed in during post-production).
Continuity mistake: When Sonny is giving Julian a bath, in the shots where Julian is closest to the camera, you can see a wide gap between the bath and the camera and even the side of the bath tub, as if it's in the middle of the room. In the shots behind Sonny, the bath is right next to a brick wall.