Visible crew/equipment: When Peter wakes up and discovers he can't see through his glasses, you can see a phantom hand on the left sliding out of view in the mirror. This happens the last time Peter tries to see through his glasses. It's not a reflection of his hand due to the angled edge - it's on the main part of the mirror. (00:18:05)
Visible crew/equipment: When Spider-Man is rescuing Mary Jane from falling to her death from the balcony, he catches her and spins his web to the balcony to save her and they bungie to just inches from the ground. As they are preparing to bounce back up the shot rotates 90 degrees and you can see the counter weight that pulls them back up coming down to the ground. It's a weird one, this - there's a sound effect as the weight comes into view, so it's meant to be there (or else the sound's just a cover), but it can't be anything he attached his web to, as it was stuck straight onto the balcony. If it's falling, they should be too - his web's not pivoting around anything. (01:06:50)
Visible crew/equipment: When the fire breaks out in the building, as the firetruck goes by you can see the reflection of the camera crew on the truck, including a man wearing a white shirt. (01:22:00)
Visible crew/equipment: At Thanksgiving dinner, when Aunt May looks outside when she sees something, the reflection on her glasses shows what appears to be a green screen. (01:26:00)
Visible crew/equipment: In the school fight scene where Peter beats Flash by punching him and making him collide against a teacher, his tray falls on his face. In that precise moment a camera with a hand on it can be briefly seen on the left side of the screen just a few moments before the shot points downwards.