The solution I have found to this problem is:
On the summary page in iTunes for the device you are trying to sync, make sure that "Sync only checked songs and videos" is checked.
step 2: unselect everything except one song / video. Let it sync, which it should now. Once the sync is sucessfull and done, then go back and select all the stuff you want to move over and try again. This time it should work.
The way I see the problem is this, I tried to sync to a different computer than I did last time. It told me that when I do this it will delete everything I had on the iPad / iPhone already, and the capacity bar slides down to about nothing. However, it didn't really delete anything YET and is still semi-full of stuff from syncing with another computer. When you try to add a bunch of media and sync from the new computer it fails with a message like "iPad cannot be synced because there is not enough free space to hold all of the selected items (additional 2.4 gb required) and yet it shows 5.4 gig free. Well, it's not free yet, it didn't delete all the stuff it said it would delete because the sync with the new computer didn't happen. The capacity bar reset it's size, but the iPad really is still pretty full of stuff. It's failing because it shows 5 gig of free space after you've picked your media, but really it's too full of media from the previous computer. Hard to explain in writing.
Unchecking everything but 1 file will let it do the sync, because it can sync and move that 50 meg music file into the remaining 2.4 gb of free space that really only does exist.
WHEN it finally does that sync it will clear out all the stuff it said it would when you first started. So, all the media that was filling it to a point it only had 2.4 gb of free space is NOW finally gone. NOW it really does have a lot of free space, unlike what that lying junky capacity bar was saying it would have.
So, now that it got rid of all the stuff and you have plenty of space now, go back and select all the media you can fit on there, while watching the capacity bar. You still cant put 16 gig of stuff on a 16 gig iPad, but at least now you can put 12 gig of stuff on their without it saying it needs 2.4 gig more room while showing 5.4 gig of free space.
*numbers are just examples, not real math*
Hope this helps -- it worked for me.