Backup via iTunes and do a DFU restore. This teds to fix most software issues.
Dropbox is working fine for me and scads of other folks. And yes a DFU restore is a hassle but so is a crashing app. It could be very well be something with the amount of files but for that you'll need to wait for DropBox to update their app.
Have you tried contacting DropBox?
Yeah it synced with multiple desktops but this didn't give any issue previously. So thats not it...
This started tobhappen when I added alot of pictures to my camera roll.