In the Safari, Help menu, select "Installed plug-ins". Any ADOBE PDF stuff there (not flash stuff, not webkit stuff)? If so, deleting (or maybe updating) the Adobe pdf plug-in might solve your problem. Safari Plug-ins are normally found in
Apple has long been noted for its ability to deal with PDF files. In particular, if you have to download them, Apple's Preview application can read them. You should not need any application from Adobe to deal with PDFs.
You can even create PDF files on your Mac by doing File > Print > [Choose the PDF dropdown near the bottom left] > Save as PDF ...
Are you actually using Acrobat or just the Adobe Reader? If you are just using the reader on your machine try updating to the latest version and see if that helps. If not then navigate to the folders that Charlie mentioned and delete the AdobePDF plugins. Yes and as Sberman mentioned unless you have a specific requirement for the Adobe Reader you are better off using apple's Preview app.
I've been having this same problem with saving pdf files File - Save As from the top Toolbar on my laptop.
I would constantly get messages - There was an error opening this document. The file is damaged and could not be repaired.
But at last I have managed to find a simple way around it.
Firstly, without downloading the pdf, I printed the pdf file direct from the Safari page by using the Print icon on the grey lozenge that appears centrally three quarters down the screen.
Then I discovered that if I save the pdf using the Save icon from this same grey lozenge on the Safari page I can open and print this pdf version from my desktop.
I've tested it with a couple of different pdf files and these methods work using the grey lozenge icons but the same pdfs files don't work using File - Save As on the Tool Bar.