If you look to the right of the "Sync failed" message in settings you'll see a link called "Troubleshoot". Tap that and you'll be taken to an article that explains that this is a known issue with FF 5.0 and shown a suggested workaround for it.

N.B. I have tried the workaround but so far with no success. Really hoping there's a fix for this bug out soon!

As best as I can make out, the current version of Firefox for iOS does not have the capability of syncing with a PC. Am I reading this info correctly? If so, does anyone have any idea when a new version of iOS that has this function will be out? Very frustrating!