Well it seems that your queue items might be partially processed.
For example If my Agent processes a queue Item to update couple of table sequentially and it is successful in doing so for one table and fails for other then we will get Items in broken-queue.
For verification you might be checking the only Update that happened correctly.
From your above error it is evident that there are sql errors and hence you see it in broken queue.
Please trace agent and check what has gone wrong.