One moment of humor that, in addition to being laugh-out-loud funny, actually seems to have been intentional is the usually ever-hammy Doom's reaction to stepping into a room to do some Evil Gloating over the Fantastic Four, only to realize mid-sentence that they've escaped and are long gone:
The Jeweler tries to keep Doom away by threatening to kill Alicia. His own prisoner. With no connection to Doom whatsoever. Victor's only response is a mildly confused "...So?".
How do you show the Thing beating up some scientists when you don't have the time or money to do a fight scene? You do this.
Dr. Doom uses charades to spell out whatever he's saying due to the mask making most of his dialogue incomprehensible.
When the Human Torch blocks the Colossus laser at the end, it knocks him around in circles with incredibly bad CGI. Even funnier is that if you go frame by frame, the laser goes up his butt at some points.