When Mary Jane is singing on stage at the beginning of the film, the audience applauds after the first couple of lines. In the next shot, no one in the audience is clapping, though the applause can still be heard.
When Peter starts to place a call on the pay phone before speaking to his landlord, the coins drop directly to the coin return. Then, when he actually hangs up, there is no sound for the coins being returned.
Whenever Spider-Man removes his mask, his costume (both red and black versions) has a turtleneck collar that goes up to the middle of his neck. Whenever his costume is shown underneath his clothes, the collar is much lower.
When Peter attends Mary Jane's opening performance and then takes her to the park, he's wearing a light blue shirt that changes from "button-down" collar style (unbuttoned - you can see the buttons under the collar flaps) to "plain" collar and back to button-down (unbuttoned again, but you can't see the buttons this time).
When Peter goes to tell Aunt May he is going to propose to Mary Jane, Aunt May starts to hug Peter with her head over his left shoulder. In the next shot from another angle, her head has shifted to Peter's right shoulder.
When Harry and MJ are cooking together, after the food gets spilled, the two of them look at each other, and MJ puts her hand on the left side of Harry's face. In the next shot, it's on the right side.
In the scene at Peter's apartment building the first time after he yells at his landlord, Peter places a call on the pay phone. First you can hear the coins dropping right through to the coin return as Peter drops them in, then there is no sound of the coins being returned when Peter hangs up the phone.
The first time Peter calls M.J. her voice message says 'Hi, it's M.J., sing your song at the beep. Beep!". Later in the film he calls her again and her message now goes: 'Hi, it's me, sing your song at the beep!' with the phone providing the second beep. While it possible she changed her voice message in the interim, this is more likely a continuity error.
When Harry and Peter meet in the coffee shop, just over Peter's left shoulder, the same three extras (two women together with winter scarves and a man holding a cup) loop to and from the counter several times over the course of the scene.
After the crane first crashes into the building, Gwen helps one of the other models up. The model is then seen standing next to the photographer several feet away, and then is once more behind Gwen in the next shot.
In the scene just before Mary Jane throws a hollow brick onto Eddie's head, his back is briefly shown where it can be seen that he is not wearing any dress under his venom suit. But later at the end when Spider-man tries to save Eddie by pulling him out, his dress comes back on him.
When the Sandman throws a car into the street, it clearly hits one car that turns sideways, then goes through the center of the street. Two cars behind the first hit, however, are pushed to the side, and the mechanism pipe that moves the cars is clearly visible.
A part of the movie features the Cleveland Trust Rotunda in the background where one can easily read "Cleveland Trust" inscribed on the Romanesque structure, although the movie is supposed to be set in New York city. Two other unique Cleveland landmarks are also briefly visible - Terminal Tower, and the marquee entrance to Playhouse Square Center.
Captain Stacy is shown wearing a variety of medals above his shield (badge). The green bar with gold stars, and the plain green bar should be worn at the TOP of his shield, above all the other bars, (not halfway down), as they represent the Medal of Honor and the Combat Cross. (The NYPD's Highest and Second-Highest awards).
The first time the Symbiote covers Peter's Spider Man suit and "copies" it, Peter isn't wearing the spider man mask, however the symbiote copies the mask exactly, as if Peter were wearing it. However, considering the symbiote affects his mind and amplifies his emotions, it's possible the symbiote copied the suit from Peter's memory.
Eddie Brock is the new guy trying to get a job at the Bugle, but in Spider-Man (2002), Jameson and Robertson talk about a photographer named Eddie who already works for the Bugle. However, they never said Eddie Brock, so "reintroducing" the character does not break continuity.
The final edit doesn't show how Brock knows about Marko's daughter (this plot hole is explained in a deleted scene on the DVD.) However, given Marko being on the run from authorities, and a manhunt going on for his capture, it is not unlikely that his story was broadcast on the news, and this story could have contained details about Marko's past life/family members/history/etc.
The main camera Eddie shoots on is a Nikon D50, which is a digital SLR (the LCD screen of the camera complete with "Nikon" logo at the bottom is also visible for a short time in one scene). Although it's a digital camera, it makes a distinct sound, like a mechanical film feed. In fact this is the sound of the reflex mirror moving for each shot, which all SLR cameras (digital or not) make.
When Harry and Peter are playing basketball in Harry's house, Peter hits the vase. When Harry grabs the basketball the ball is apparently sticking to his fingertips. Holding a basketball like this is difficult, but not impossible for a very-skilled basketball player (or someone with Harry's newfound superhuman abilities.)
When Peter takes Gwen to the jazz club and they sit at the table, you can clearly see Willem Dafoe (who died as Norman Osborn in Spider-Man (2002)) sitting and enjoying himself as an extra at the table behind them. (This use of major cast members doubling as extras is a director-trademark of Sam Raimi, which recalls his first low-budget movies.)
When Spider-man shows up for the main fight scene, a lady holding a girl says "look!" and everyone turns around to see him. But the lady and girl are facing the other direction, so she couldn't have seen Spider-man coming.
When Peter and Mary Jane are lying in Peter's spider web near the beginning of the movie, as the scene is zooming out you can clearly see a strand of web made out of chain near the bottom of the screen.
When the cop holding a shovel is walking on top of the sand in the truck concealing Sandman, you can see the right hand edge of the platform used to stop him sinking into the sand. He stops right at the edge of the platform to raise the shovel.
When Spider-Man chases Sandman into the storm drain, he tears the grate out of the street, also ripping out concrete and causing cracks in the pavement. When the camera angle cuts to looking up from the storm drain, there is a nice square hole as if the grate were lifted out neatly.
Several scenes show police officers having an "N.Y.P.D. Police Department" patch instead of the actual patch which would read "Police Department, City of New York". In addition, the real police officers (non actors) can be seen wearing the genuine patch in scenes filmed on location in New York.
When Spiderman is being pummeled by the Sandman while being held down by Venom, underneath his eye, his mask is being held together by a couple of pieces of thread. When he is shown in later scenes, though, his mask has about 3/4 of an inch of fabric left holding it together.
Before Peter and Harry have their fight at the Osborn mansion, Harry pours himself a martini and is still holding it when he turns around to talk to Peter. After Peter punches him, the martini disappears.
The explosion when Venom was killed between the metal pipes looks quite unrealistic - it's blast radius doesn't even reach Spider-Man as is somehow limited by the circle of pipes, which have deformed from the explosion. The same grenade, when Spider-Man threw it to Harry, did clearly more damage.