I got too into it and did some deep analysis on 3 videos of the explosions:
Judging from this, it cannot be confirmed who exactly caused the hospital explosion, but there are some things of note:
1) Explosion 1 and the hospital explosion occurred at nearly the same time, but are very far apart. The pitch black night and lack of city lights in Cam 1 makes it look like they're related, but they're not.
Explosion 1, as seen in Cam 2, is quite close to the northern border with Israel, while the hospital explosion is in the heart of Gaza City.
2) This also disproves theories that the missile in Cam 1 broke apart and fell in two or more sections causing both explosions.
3) Judging from the distances of both explosions to Cam 1 and Cam 2 respectively, it can be determined that the slew of missiles being fired from Gaza toward Israel in Cam 2 and the lone missile seen in Cam 1 are not part of the same attacking force, and are pretty much firing AT each other. It appears that the one misfiring/malfunctioning missile was launched either from Israel or very nearby Gaza's northeast border with Israel.
4) The faint flash in Cam 3 proves Explosion 1 was very far away from the hospital, and has that controversial "JDAM" sound which is unlikely to come from bits and pieces of a broken apart missile.
Shame that Cam 1 and Cam 2 don't have audio and cannot confirm if the audio of Cam 3 is authentic.
In conclusion: inconclusive. The misfiring missile may not have been at all related to the hospital explosion, but it does not seem very likely that it was fired from Gaza.
