This error may occur when a payment has been entered both in Sage Intacct and Bill.com prior to a sync.
Cannot overpay a bill or Cannot overpay an invoice
This is expected and correct behavior, and should be resolved by clicking the Fix link on the left, and then clicking the Next button.
Normally that would be the end of it - but in this case the error persisted on each subsequent sync. For AR payments, this also caused duplicate payments to be created in Bill.com.
The problem was caused by a bug in Sage Intacct that existed prior to the Winter Release, and has been fixed as of 03/11/15. The bug tricked the sync into believing a given payment needed to be synced on each and every sync, rather than syncing once and being finished. This is what caused the error to persist and the duplicate AR payments to appear.