Dawson Casting: 27-year-old Andrew Garfield and 23-year-old Emma Stone as the teenaged Peter and Gwen — though, truth be told, Garfield pulled the role off unlike most actors above their teens.
Like Tobey Maguire, Andrew Garfield played a teenager despite being in his late twenties. In fact, Maguire first played him at 27 and Garfield was 28, so he's actually older than he was, even though this Peter actually spends almost all of the movie as a high-school student, not just the first act. It seems to work, though, as Garfield certainly doesn't look that old.
Same applies to Max Charles, the kid who plays Young Peter. He's nine years old but Peter in the beginning is around 4.
Emma Stone, age 24, plays another high school student. Emma Stone was questionable, but still believable.
Deleted Scene: Dr. Ratha was attacked by the Lizard. However, the scene doesn't fit into the final continuity of the film.
Averted with Rhys Ifans as Dr. Connors, as the character's thick accent indicates he's really British. (Although this is also a minor example in that he uses a more generic English accent rather than his own Welsh one.)
Subverted with Andrew Garfield as Peter Parker/Spider-Man, given that he is British-American and was born in California but grew up in Surrey, England & subsequently has an English accent.
Jossed: When the first film came out, people suspected that the Man in Shadows was Norman Osborn under the guise of the Green Goblin. However, Rhys Ifans and Marc Webb confirmed that he was a different character. They did clarify that he is associated with Oscorp.
Older Than They Think: Many fans were vocally upset that Uncle Ben never says his famous lines: "With Great Power, Comes Great Responsibility" the thing is in the original comic Uncle Ben never said that either those lines were part of the ending narration by Stan Lee.
One of Us: Emma Stone really wants her character to die eventually, because she became a big fan of the comics while doing her research for the part and feels that the death is such an important part of the mythos. She got her wish in the end.
The script for Spider-Man 4 which caused Raimi to leave the series and Columbia Pictures opt to simply go for a Continuity Reboot rather than find a new director & cast to continue Raimi's story. For more info on the script itself, see here.
A lot of footage that featured Dr Connors wound up cut from the film, including a brief appearance of his son Billy & a sequence that saw Spider-Man encountering Dr Rathra in Connors' lair after the fight at the school and ultimately ended in the Lizard killing Rathra. These scenes were later included on the DVD.
Word of God: The first thing Spider-Man shoots a web at and subsequently proceeds to swing from just so happens to be a helicopter as a nod to the incident in the comics where Spidey swings past the Empire State building on an off-panel web. It is explained in the letters section of a later issue that there just so happened to be a helicopter passing by at that moment.