I recently posted a bit of a bad OSP board with the conclusion that it was only worthy of scrap. Over on the Circuits Assembly blog, Mike commented that if the board was expensive enough, he'd rework it and make it usable. He gave a pretty detailed description of the process he'd use too. And he's absolutely right. Here's a picture of the full BGA land pattern on the right. You can see just how many pads were messed up and how random the pattern seems to be.
While not everything can be fixed, a lot of things can. It all depends on the cost of remaking vs. reworking, the time to remake vs. the time to rework and what you need ultimately in reliability. In the prototype world, we do a lot of work to just make messy things work simply because of the time constraints.
Here's an example of something yucky that we made work. We've also cleaned tarnish off of silver boards and done a bunch of other things to recover from difficult challenges. As always, when we do do something like this, you're really in test-pilot mode.
Rolly polly fish heads
Eat them up, yum.