Simple solution with regedit:
Delete the "Recent Directory" registry key:
\Registry\HKEY_CURRENT_USER\Software\Blizzard Entertainment\StarCraft II Editor Beta\Recent Files\Recent Directory - Open and Save Documents
If that's not enough, delete the entire "Recent Files" registry folder:
\Registry\HKEY_CURRENT_USER\Software\Blizzard Entertainment\StarCraft II Editor Beta\Recent Files\
And if that still doesn't fix it, delete the entire StarCraft II Editor Beta registry folder: (This will reset all your editor preferences to default though.)
\Registry\HKEY_CURRENT_USER\Software\Blizzard Entertainment\StarCraft II Editor Beta\
This should fix it up, thanks to 3ICE for figuring it out. If not, attach your crash logs in a reply here, please.