Comment 10 for bug 719843

I think I know what this issue is, not that the update doesn't occur, but moreso that the old copy stays in the screen even though the new one is added.
I wrote the modify and delete code a long time ago and since then we received pagination support in USC which meant we needed to tweak the existing submit/flag/vote code to prevent duplication after a successful submit (see bug LP: #794060) with the new way the callback works after pagination was added.

I don't think we have made the same tweak on the modify/delete code since then so it's probably using the old callback method and 'duplicating' the reviews by not removing the original before inserting the updated version.
There are some helper functions in the UIReview class that should make this very simple to fix.