When I receive a PDF attachment, the Gmail app only gives the option to preview it, not download. It opens in the default PDF reader (I have Adobe's reader).
How can I save the PDF instead?
Attachment2SD will do the trick.
After you install it when you click on the PDF attachment in the Gmail app it'll pop-up the "Complete Action Using..." dialog. Choose Attachment2SD and it'll download to a directory on your SD card, where you can immediately open it or save it for later. This works with all kinds of files, not just PDF.
Don't use the Gmail app, instead use your browser, go to gmail.com, mobile or desktop view doesn't matter,
open the mail you want to download the pdf from
click on the pdf icon and it will be downloaded automatically.
About doing so with the Gmail app specifically, I've no idea, and that was how I dodge the pdf problem.