For me, it depends. Which signature do I need? If a doc is missing that requires the borrowers signature, I'm not going to buy it. If an assignment is missing, but I can get it replaced or substituted with a missing doc affidavit, I might. What you want to do is be prepared for the borrower to demand the originals. I'm having that happen to me currently. Usually, it starts with a question and answer phase where they ask if you have the originals. Then they can request them if the court process gets to the extreme stages. So make sure you have all the originals from the borrower.
If the missing docs are recorded at the county, that makes it easy. I've lost some docs in the mail, but once it gets recorded with the county, I'm not that worried about it. If it isn't recorded, then I would look to see that the entity that originated the doc is still around to see if they can replace it. If they aren't around, things get more complicated, but not impossible.
So there is my risk factor level.
Borrowers signature needed? Won't buy it.
Doc recorded with county? Will buy it.
Doc not recorded, entity still exists. Might buy it. Depends on the deal.
Doc recorded, entity is gone. Probably won't. Depends on the deal.