Revealing mistake: Peter, scientific genius, needs to watch Youtube to understand how batteries work (and will need Gwen later to remind him the obvious relation between magnetism and electricity). As he watches the video, we can easily see it's a dummy page; it has 257,529 views, but two subscribers, and with 92 likes and 0 dislikes has still the bar that shows the like/dislike ratio that is about 4/5. The video is stupidly short, just 20 seconds that say nothing about the topic, and when it's 2 seconds from ending it still goes on off camera for about 6 seconds. (01:03:45)
Other mistake: When Peter looks up "Roosevelt hotel", the map result shows "Map data ©2013 Google." The movie was shot in 2013 but takes place in 2014. (01:01:30)
Revealing mistake: Electro grabs two cables and unleashes the power of dubstep making every billboard and sign fall. In the shot where the billboard for Mamma Mia and Jersey Boys begin to fall, several extras are running towards the camera and there are a few (like a woman to the left, wearing a white pantsuit and a light purple vest) that are laughing as they supposedly escape terrified. (00:58:30)
Continuity mistake: Enraged because Spidey is being filmed by cameras, and he is not (best villain motivation ever), Electro sends a wave of electricity towards him. Spidey jumps over police car 7703 (the one that he dented landing spine-first in it earlier) but the slow-motion sequence that follows takes place featuring car 1206. (00:56:40)
Continuity mistake: When Electro approaches the cables in Times Square, in the overhead shot we see that the person closest to the grate he targets is standing one row away from it. The following shots are consistent with that, even if we can see that there are more people. When he opens the grate in another angle, that person is standing right next to it. And when he digs his hands into the cables, some person with khaki pants is walking across the metal grids, but he wasn't there before. (00:51:35)
Continuity mistake: After Gwen says "I'll be moving to England", she takes a breath, swallows, closes her mouth, but in the next shot her mouth is open. (00:50:40)
Continuity mistake: When Harry at the board meeting sarcastically paraphrases the Connors incident mentioning the "giant lizards" you can see Felicia Hardy in background is writing down things, but she isn't in the previous shot. (00:37:05)
Continuity mistake: At the board meeting, Harry is playing with his father's electronic seal in a way that displays towards the camera the side with the Oscorp logo. But there are two different camera angles from opposite sides, it can't be facing both at the same time. (00:36:55)
Revealing mistake: When Gwen catches Max's elevator in a rush, she clutches to her chest the same mug that when she went through the door was practically horizontal. Luckily it's one of those movie empty mugs people carry for no reason. There's a similar scene the day after when she carries an empty mug - a different one, incidentally - but that's when she is running away from the security and the mug is supposed to be empty. (00:28:20)
Continuity mistake: Gwen's phone call;Spidey holds the plutonium in a different position in each shot - at the end he even just has it standing perfectly vertical on its own. After the first two shots -when his arm goes from behind the grill to under his chin - we are not talking about consecutive shots anymore and the camera cuts away each time for over two seconds so it is technically possible he'd change position every time, but it randomly goes from above the grill, to behind, front, and perched on it. (00:11:25)
Continuity mistake: In the second part of the chase, Sytsevich drives off leaving all the police behind and all the plutonium falls from the rack except the second container from the left in the top row. During Spider-man's antics in the back of the truck you can see the container about to fall (and eventually falling) from the third hole from the left. (00:10:50)
Continuity mistake: Aleksei Sytsevich abruptly stops the truck creating a pile-up of police cars. There's a close-up of a container of plutonium falling off an otherwise full rack, but the following part of the scene shows the rack half empty, and in any case the one contained that fell in the close-up was the bottom left one, in the rest of the scene the one missing from that column is the top left one. (00:10:25)
Continuity mistake: When Spidey wastes 20 seconds of valuable time for the ever important task of fixing Max's combover, he says "Lick that", and in the next shot Max does not lick 'that', but 'the other one'; Spidey put in front of him his left hand but the reverse shot shows Jamie Foxx's tonguing Spidey's right phalanges. (00:10:00)
Continuity mistake: When Aleksei Sytsevich says his own name and cackles, we see the other marauders jumping on the Oscorp truck. There's a shot from a crossroad with a pedestrian wearing a grey suit that looks at the police car in pursuit, and at the street corner there's a woman by the garbage bin; the camera angle changes and the people at that corner have changed. (00:08:10)
Revealing mistake: In the airplane fight, heavy objects (and people) get sucked out of the door once the cabin is depressurizing, but the cables and the mask tubes on Richard's side stay softly curled and unmoving throughout the scene. (00:06:10)
Other mistake: Richard Parker is running away from Oscorp after triggering an alarm at either 6:30 or 9 PM - the movie is contradictory on which one. He goes home to quickly pack and get his son, and then goes to his brother's place to dump him there. The next scene shows him and his wife discussing the situation, including where to spend the night; they are mid-flight to Wisconsin and it's daylight.
Continuity mistake: When Mary and Richard Parker says goodbye to their son, the scene is similar but also different from the previous movie; she delivers her line with a calmer voice and doesn't stroke his hair in the jittery nervous way of the original. The dad's farewell to Peter is also longer and here they touch hands. (00:02:25)
Continuity mistake: When Peter looks at Gwen's mementos, the photo he had in hand and the USB key both change position between shots. (02:07:50)
Continuity mistake: Peter is absent-mindedly listening to the news while Aunt May is putting away some objects. There's a cut while the speaker says "return of the web-slinger" and May who just had put down some letters is suddenly lifting a book. (02:06:25)
Continuity mistake: The one kid Spidey helped is looking at the window during the news story about Rhino breaking out of prison. He leans forward, but he's in a different position between shots, and his wind turbine is powered up only in the last shot even if it was still two shots before. (02:06:15)
Answer: Peter could have contacted the police anonymously.
MasterOfAll