Apple’s Fontbook application can examine fonts for corruption. Unfortunately it’s buggy, poorly-documented, and often flags valid fonts as having problems. But it’s a start. Sort good from bad family by family, and back them up so that you have clean copies if this happens again.

Upgrading to a new version of Font Explorer does sound like a good idea.

You can deactivate half the fonts, and see if the crashing stops, then deactivate the other half. When you know which half causes it (assuming there's not a ton of corrupt fonts), do the same with half of that half, and so on, till you narrow down the culprits.