Visible crew/equipment: When Peter approaches Happy in the beginning, you can see the camera reflected in his glasses. (00:06:26)
Other mistake: A poster in the school states that the Academic Decathlon takes place on October 14-15. But later on in the movie, another poster says it's on September 14.
Suggested correction: Was in a similar thing in HS. Not too surprisingly, we had more than one event throughout the year. In fact, I've never heard of an extra-curricular with only 1 event. Likely 2 different meets.
They said later on, though, and that would go into the next school year, which is weird for most extracurriculars to have pre-planned events for the next school year.
Continuity mistake: When Peter and Ned are removing the tracking device from Peter's suit in the hotel in Washington D.C, Peter has a flashlight in his mouth. He removes it, but in the very next shot, it is back. Later, as he puts it in his mouth, it switches to his hand, and back to his mouth in between shots. (00:47:50)
Continuity mistake: In the ferry fight, in one shot nobody is behind Spider-Man, but in the next shot Vulture and another man are.
Continuity mistake: When Peter steals Flash's (Dad's) car and hits the bikes that were on the side of the road, there is no damage on the front of the car in the next shot.