How can I make sure my photos aren’t damaged after copying them from a faulty SD card?

I’ve copied pictures from my faulty SD card. Most of the photos seem to be ok, but some have big gray parts where originally the photo was.

How can I make sure that all the photos that seem to be ok, are really ok?

Can it be a problem to have damaged .jpegs in the same folder as the correct pictures?

What can I do about that? I want to lose as little as possible.