Contested Sequel: Edge of Time is seen by several fans as inferior to Beenox's last Spider-Man game, Shattered Dimensions. While some do defend it, many admit that losing Noir and Ultimate was a steep blow.
However, while this game loses some of the simplicity and accessibility of the first game, it gains a tighter and more mature narrative, improved voice acting from the two best Spidey voice actors (go ahead, try to envision Harris & Gilvezan reprising their roles rather than Barnes & Keaton. Most of the dialogue wouldn't work nearly as well, or would sound awkward with their voices), better dialogue, more interactions between the Spider-Men of the game than just the ending, and a few twists most wouldn't see coming. It's easy to assess this game as having a better story than Shattered Dimensions, but maybe failing to live up to most of the hype that it created due to not being exactly the same.
Demonic Spiders: Stunners: they emit shockwaves that are nigh impossible to avoid (your only option is to regularly abuse either Spider-Man's Hypersense or 2099's decoy ability), they fire very quickly, they stun you so that you can barely move or attack for several seconds, they have a shield that prevents you from directly attacking them to stop an attack, and they're fairly common.
Crashers are a close second: a Heavy that takes a ton of hits to kill, doesn't flinch when you hit him, attacks quickly, attacks in a very wide medium-ranged arc that's tough to dodge, and can knock off a third of your health in a single hit. They almost always have enemies with guns for cover and they can teleport to chase you down if you try to clear out the other enemies first.
Fridge Brilliance: Not having Noir And Ultimate was disappointing, but it does make some sense. Noir knows nothing about technology, and Ultimate would be just a copy of Amazing without the black suit.
Good Bad Bugs: In the Wii version, by punching the air in the time-gate room after you beat the first phase of Anti-Venom as Amazing Spider-Man, Amazing's lines and quotes will act like Anti-Venom is still in the room, despite him being launched into another room.
Hilarious in Hindsight: One of the available outfits is the suit used by Miles Morales, Peter Parker's successor in the Ultimate Universe. Flash-forward to 2012 with Spider-Men, where the 616-verse Spider-Man finally gets to meet him.
This happens when Spidey says that he finally knows how it feels to come Back from the Dead, as a joke referring to how death isn't really anything in the Marvel universe (even specifically citing characters like Colossus and Captain America). Also within 2012, he would get his body swapped and taken off of life support by Doctor Octopus, dying.
In Superior Spider-Man #15-19, changes in the timeline have caused Miguel to be stranded in the present and Alchemax to have been founded in the present day, turning the plot of the entire game into this.
Miguel's words to Mary Jane about her and Peter having their whole future together is near heart shattering after One More Day.
Padding: It takes two full hours to get to the Anti-Venom Boss Fight while absolutely nothing else happens. The remaining four hours of the game have little in the way of story developments and you spend long stretches doing nothing but run around trying to fix the time machine.