There's a strong undertone about the importance of family connections, ranging from Peter's very loving connection with his Aunt May to Peter's pal Harry, who's clearly bothered by his strained relationship with a cold, domineering father. Peter is the victim of some bullying at the hands of the school's "cool" kids, but the experience further motivates his heroics on behalf of the innocent public.
Plenty of cartoon fighting, though there's no blood or gore, and nobody seems to get seriously injured. Spidey keeps a running patter going as he takes down the bad guys, which make the fights feel even less serious. Spider-Man uses fists and webs, supervillains use other unusual weapons, and some of the bad guys use guns.
No sex or nudity, though Peter does have a major crush on one of his classmates.