Why the hell did the cops at the hospital set up the (expensive, and identical to Andrew's) camera to film Andrew while he was unconscious? There's already a security camera in the room. Seems like an Ass Pull to keep a hi-res digital camera close to the main action.
Or in the confusion, someone put his camera there and accidentally turned it on. Or it was left in the closet or something, and Andrew woke up enough to turn it on by TK.
The cops put it there and turned it on. When Richard goes in one of them tells him not to disturb the camera because they "need it for their investigation." They probably saw the security footage of the robbery, including apparent TK abilities, or at any rate something unexplainable involving the perpetrator, and if it happens again they need it on record. Hell, more than likely they are involved with some government agency that is aware of the meteor-whatever, who have been following the situation since the cave in.
The kids never compare themselves to, say, Peter Parker or the Fantastic Four, and no one uses the words "superpower" or "superhero". It's next to impossible that the boys, having lived all their lives in America, with normal access to TV, cinema, etc., have no concept of superheroes or have never been exposed to any form of superhero media. Perhaps they simply don't exist on this Earth?
Maybe they just don't pay much attention to comics and the like. Andrew's a shut-in, Steve's probably preoccupied with his school work, student government campaign, and football practice, and we don't know Matt's hobbies.
Don't they put on Star Wars music while force-lifting the Legos?
What was Andrew doing in the time between blowing up the hospital room and trying to throw his father out? There was enough time for the news crews to begin filming and broadcasting it and Matt driving to downtown Seattle from the suburbs, getting around several police roadblock already in place. That must have taken Matt an hour at least, when you'd expect Andrew to do his thing in seconds.
Well, It is down town, so the news crews could have already been there. Maybe (its possible there was a slow news day) they were reporting on Andrew's earlier robbery. As for Matt, we don't know where his girlfriend's house was in relation to the hospital, or when his nose started to bleed. its possible it started before Andrew's father arrived. Some of the scenes are probably out of exact order so they would make sense to the viewer.
It seems that the explosion happened while Andrew was unconscious. It could be that, for a while, he was still out of it. Only when the noises of the sirens and helicopters grew (or Matt arriving on the scene) did he wake up. He then saw his father lying next to him, flew into a rage and zipped out the hole in the side of the building.
Actually, you clearly see Andrew's eyes opening a second before the explosion; plus, he grabbed his dad's fist in mid-swing. However, it's possible that Andrew got around to doing quite a bit before Matt arrived; first of all, assuming the blast didn't kill them, he'd have had to take care of the cops that were guarding his room; then he'd have to keep the nurses and other hospital staff from interfering; then, his dad might have tried to make a run for it (assuming he was able to do so, under the circumstances) meaning that Andrew would have had to chase him through the corridors; finally, Andrew may have been in a bad enough mood to torture his dad before he decided to kill him- we don't exactly see the full extent of his injuries once Matt rescues him. Also, Andrew was badly injured and disoriented from painkillers, so that might have slowed him down a good bit.
If you look closely at Richard as Matt brings him to the ground after saving him, Richard appears to have a severe head injury of some kind. The implication being that Andrew did indeed physically assault him before trying to kill him.