Apart from the dialogue in the cut scenes, the in-game dialogue (when Spidey speaks to various characters) was pretty good. The characters sound how you might imagine in the comics. Luke Cage's dialogue is deep and street-savvy, while Kingpin's voice is brooding, cruel and calculating. Spider-Man's voice actor is pretty good as well, with the whiny, nerdy edge, similar to that of Tobey Maguire's voice for the character.
Having said that, another gripe I have with the game is the total lack of Peter Parker. We never see the civilian side to Spider-man's life. There is no running around the office of the Daily Bugle as Pete, talking to J. Jonah Jameson or Joe "Robbie" Robertson, like there was in the Spider-Man 2 game. I felt this was a shame, as it detracts from one of Spider-Man's appealing qualities; his humanity and struggle to maintain a (super)work/(normal)life balance, which I think are what has made him such a popular comic book character.
Moving on, the music in the game is really good. The orchestral score, which can be heard fully at the menu screen (and the beginning of the above video) provides a sense of gravitas that fits the epic nature of the storyline. Tense and darker music is heard during important scenes, especially when in the Black Suit. When missions are completed, a victorious fanfare is played that simply makes you feel good.
The ingame sounds, such as the yells of enemies, punches and grunts are all handled fine. But the best of all is the classic "THWIP" of Spidey's webshooters. It's cathartic and engrossing, and care was clearly put into making this an awesome sound.
To web-swing, the player flicks the Wiimote down (like Spidey would flick his wrist down) and a thwip is heard from the speaker in the Wiimote (like Spidey would hear the thwip from the webshooter on his wrist). This was just so cool, as its a great way to add to the immersion of the game and lets the player "feel" like they are Spider-Man!