(at around 26 mins) When Aunt May is talking to Peter about doing the washing, she is holding a sandwich with lots of lettuce leaves sticking out of the top. She passes it to Peter and the next shot shows him holding the sandwich but it has no salad leaves of any sort.
(at around 1h 55 mins) Electro has a control chip placed on the right side of his head. However, during the end of the power plant battle, the chip has switched to the left side of his head.
(at around 10 mins) When Spider-Man talks to Max after saving him, he holds up his left hand and says, "Lick that!" In the next shot, he is holding up his right hand and his left hand is on Max's shoulder.
(at around 1h 1 min) After Peter listens to his ear buds while lying on his bed, he sees his father's briefcase in his closet. When he gets up, one of his ear buds falls out, but the next shot when he's walking to the closet door, both ear buds are secured in his ears.
(at around 55 mins) In the Times Square fight sequence between Electro and Spider-Man, Electro sends a bolt of electricity to ram Spider-Man into a police vehicle, denting its door. In another scene seconds after this one, Electro sends another bolt towards a crowd on a staircase, and there, in a slow motion sequence, Spider-Man tosses up the same vehicle to block this bolt, but the vehicle is not damaged, with no broken door.
(at around 9 mins) When Spider-Man is trying to regain control of the plutonium-238 shipment, an onboard computer warns that the plutonium is highly explosive. Plutonium-238, however, is known for not being fissile. Instead, it is used for radioisotope thermoelectric generators because its short half-life makes it release enough energy to stay constantly hot.
The two planes on a collision course would never have been in any real danger. All commercial aircraft carry a device called TCAS (Traffic Collision Avoidance System). In the event that two airliners are on a possible collision course, the transponders of each plane will have communicated with their counterparts and each plane's TCAS will give the pilots the necessary climb or descend instructions to prevent a midair collision once the planes get within 100 miles of each other. TCAS does not rely on any ground communication, so a power outage would not interfere with it.
(at around 1h 23 mins) The British Union Flag hung from the ceiling before Gwen goes into her interview is backwards. In the correct configuration, the the broad white area of the diagonal white stripe is always clockwise to the right of the narrow red diagonal stripe.
Two airliners are depicted as heading towards each other, practically nose-to-nose. This would not be possible because of flight regulations that place a distance in altitude of at least 1,000 feet, depending on compass heading. For example, a plane flying northeast would fly at an odd-numbered altitude plus 500 feet whereas a plane flying in the opposite direction would be at an even-numbered altitude plus 500 feet.
(at around 1h 55 mins) Pilots of airplanes on a collision course would all make an avoidance maneuver to the right. In the movie they made a left turn, the controller's heading direction shouldn't make any difference while in sight. However, if the visibility had been good enough to see each other in time, there would have been no risk of collision; which demonstrates that it was not good enough.
(at around 13 mins) During the opening chase when Spidey hangs the last container of plutonium from a lamppost with his webbing, Aleksei easily grabs it, breaking the web. When Spidey immobilizes him by webbing his hands, he can't break the webbing. This is because he used only just enough strength of webbing to hold the weight of the container.
(at around 16 mins) Gwen reminds Peter to join her family for dim sum at 8 PM in the evening. Dim sum is normally only served in the mornings and at lunch, not as dinner. However, there is no reason for a restaurant which caters for Western diners, to rigorously follow Chinese tradition.
(at around 42 mins) When Harry and Peter skip stones while rekindling their friendship, the stones bounce across the water, however, there are no ripple effects.
(at around 24 mins) When Max is reaching for his birthday cake in the refrigerator, the light reflects off of his missing tooth, showing the black material which covers his real tooth.
(at around 1h 3 mins) When Peter looks at the YouTube video on batteries, on the bottom right the video is said to have no dislikes yet there is a grey shading on the 'likes' bar above.
Several times in the movie, when Peter is hallucinating the vision of Captain Stacy right before him, while wearing his Spider-Man mask, the reflection of Captain Stacy is visible in the eyes of the mask. Since Captain Stacy is obviously not there, it wouldn't make sense for him to be visible in the Spider-Man mask lenses.
The final scene when spider-man returns to face the rhino the shadows (from the buildings) are missing in some shots and fully extended in others.
(at around 41 mins) When Harry Osborn and Peter Parker are walking though the park, the camera crew and boom are reflected in Harry's mirrored sunglasses.
(at around 1h 10 mins) When Peter and Gwen hide in a storage closet at the Oscorp building, light beams stream through the holes in the door. For about two seconds the studio light used for this illumination is clearly visible behind Peter's head just outside the door (unless Oscorp has unnecessarily huge spotlights sitting in the middle of its hallways).
(at around 11 mins) When on the phone with Gwen while running late for his graduation, Spider-Man tells her his rapidly changing location is "First and Broadway, Second and Broadway, Third and Broadway." In Manhattan, Broadway does not intersect with First or Second Street.
The globe structures at the top of the Brooklyn Bridge that Peter and Gwen stand atop do not exist on the bridge in real life.
(at around 1h 4 mins) It is extremely unlikely that Peter - who is incredibly intelligent and has invented the web shooters on his own - would have to watch a YouTube video to teach him that batteries can explode if they are overloaded.