On iPhone/iPad, can you view a PDF sync'd in iTunes? A podcast I subscribe to has mp3 files and PDF files side-by-side. They all sync together into iTunes. On the Mac, in iTunes, I can double-click on either and hear (mp3) or read (PDF) what's inside.

However, when I sync this podcast and all its files onto iPhone/iPad, only the mp3 files are visible. Is there any way to get the PDF files to appear there? Seems like if they appear next to the mp3s on the Mac iTunes client, they should appear in the Podcasts screen in iOS.
Yes you can do this but the mp3s and PDFs are two distinct things that need to each be setup for syncing separately. 

So, sync your podcast/mp3s like you always do. Then you need to tell iTunes to sync your PDFs through the books tab when you have your iPhone/iPad plugged in. They will sync to your phone as a book and be visible in the iBooks application.

Unfortunately, that's just the way it works. You won't be able to view the PDFs in the iPod application on the phone, just through iBooks.