I've had the same problem on my Samsung Galaxy Tab 10.1 (WIFI) and I believe I've solved the problem (fingers crossed) without a factory reset.
Here's how:
1. Go to BROWSER - SETTINGS - ADVANCED. Select 'Reset to Default'
2. Next go the TABLET SETTINGS - ACCOUNTS AND SYNC. Delete the GMAIL account entirely. As far as I know this will erase all the GOOGLE settings on your tablet
3. Go back to the BROWSER - SETTINGS - GENERAL. Tab 'SYNC WITH GOOGLE CHROME'
4. Enter your GOOGLE ACCOUNT details and proceed as instructed.
5. Go back to TABLET SETTINGS - ACCOUNTS AND SYNC. Your GOOGLE ACCOUNT should be added again. You can select 'AUTO-SYNC'
6. tab on your GOOGLE ACCOUNT. You can now select what GOOGLE functions you want to sync. I've deselected PICASA as it slows down GALLERY (I have a lot of pictures online)
These steps worked well for me and my Galaxy Tab 10.1 is now fully synchronized with my GOOGLE ACCOUNT without error messages