I researched a lot on this and seem to be getting conflicting answers on SO and all of the web. I understand that with Section 508 that compliance DOES NOT equal accessibility
There are levels of 508 compliance, if you're talking about a government project. Some departments assign 508 scores to their developers, and it factors into your score for future contracts. 508 Compliance only requires that everything is reachable by keyboard, which is usually true, in a way. Screen readers will read everything that's not hidden, and tab keys will take people through links. But if you want a good score, you must address the intent and not only the letter of the law.
Edit: Screen readers will read some hidden elements. One method is to absolutely position an item above the screen with a negative top position. Another is to use the clip property. http://adaptivethemes.com/using-css-clip-as-an-accessible-method-of-hiding-content/ But if you're using display:none, heights of zero, and javascript toggles, many screen readers will not speak these items.
In the case of a drop-down, you are actively hiding elements from screen readers etc, so you do have to fix it, because most readers won't hear things with display:none.
You will not find definitive documentation on keyboard navigation. The reason no one will specify exactly what to do, is that there are so many potential conflicts - with the browser, the OS, etc. There are also no standards, although Aria is making progress: http://www.w3.org/TR/wai-aria-practices/#keyboard
I would not put accessKeys on a menu, if that's what you meant.
Instead see: http://www.w3.org/TR/wai-aria-practices/#aria_ex_widget
I would save actual accessKeys for major things like 'Search' and 'Home'. Adding a learning curve to your site wouldn't help the cause, if you had an accessKey for everything. If you put for example, "About Us" accessKey=A, and you had 20 accessKeys assigned to letters, it would be bad.
I've been doing 508 sites for a long time, and personally, I just don't use drop-downs. It's far simpler to add subpage menus. And I personally hate clicking on dropdowns. Dropdowns require a precision in clicking that just irritates me, and doesn't help with accessibility, because remember accessibility also includes people who don't click very well. Plus, dropdowns are limited in the number of levels you can have, not technically but from a UX view.
What I use:
The problem especially is in sorting information. Think how quickly you scan a long list of links, and then imagine sitting there and waiting for it to be read to you. Perhaps, organize your content into digestible pieces & let the search box do the scanning. Depends on the content.
Luck. :)