OpenELEC freezes on me intermittently in the middle of video playback, likely because the video file itself is corrupt. What can I do to bring it out of its frozen state, and, e.g. back into the file explorer (or somewhere else equally sensible)?
OpenELEC and XBMC use the Xorg server as the foundation of the GUI. By default, X can be exited via Ctrl+Alt+Backspace. Try that next time this happens; if it works you will either get spit to console or a login screen, but the video player will be dead. Unfortunately, getting the keystrokes through the lock-up may take time. So try it a few times and give that a few minutes.
I cannot promise that OpenELEC and/or XBMC have not disabled the Ctrl+Alt+Backspace default behaviour, so if this clearly does not work, have a look here and see if you can apply the suggestions. These are with regard to a Ubuntu installation, but the X server is the X server -- it's the same fundamental piece of software and can be controlled/configured using the same methods.
you may pull the power plug, wait for 1-2 seconds and connect it back again.
still, I'm not sure your problems are because of broken video files, most probably there's something wrong with your power supply, please, make sure you have an adequate power supply, able to provide at least 2A at 5V.