This doesn't really sound like a Zotero problem. Zotero simply saves files on disk.

Do the files open in Preview?

How did you get your library to this computer? By using Migration Assistant or by using Zotero syncing?

Can you open the PDFs in your web library?

Do you still have access to the old computer? If so, are you able to open the files there?

This just sounds like files were corrupted while being transferred to this computer, unless this happens on the old computer as well. (I've never heard of Migration Assistant doing this, though.)

If your files are all online, you can just search for all PDFs within your Zotero data directory in Finder and delete them, and Zotero will redownload them. But there's no reason this should be limited to Zotero files or PDFs, so if lots of your files are corrupted, that'd be a more general concern and you may want to test the old computer and, if it's OK, re-try the transfer.

OK, so this wouldn't have anything to do with Zotero. I would make a backup of any new data on this computer, erase it, and redo the Migration Assistant transfer. If you're still having trouble with corrupted files after that, you should take the computer to an Apple Store. (Don't bother mentioning Zotero, which is irrelevant. These are just PDFs on disk, which you should be able to open outside of Zotero.)