After working with PDFs for the past year or so, I have come to realize that there really is no easy way to ensure 508 compliance with an automated tool. Sure there is the Adobe built-in Accessibility Checker, and a number of third party solutions which I won't name here, but in reality manual inspection is the only way. The same is true for website accessibility. The number of tools and automated resources can really cut down the amount of time spent verifying compliance, but the only way to know for sure is with a manual review.
An automated tool can tell you if your PDF is lacking a language specification, or if the tab order is not defined, but it cannot tell you if the content makes sense in the order it is read. An automated tool can verify if you're missing alt-text, but it can't tell you if your alt-text is meaningful.
Automated tools do come in handy for identifying errors that you may have missed upon initial inspection, and they can help focus your attention in the right direction, but should never be used as the sole indicator of compliance.