Also the files need to be treated as a group of files. It's no good if the player resumes position on an individual track basis.
Well, when it works it does treat them this way. If you go to the "album" (the book) you'll see an icon next to the "current" chapter, indicating the one in-progress that you last listened to. On an iPhone, in any case.
But since I wrote that response I've found it to be wildly unreliable in terms of registering as a "remember last position" book. If it works for a given sync then it will work continuously until the next sync, at which point it may or may not break again. Most of the time I find that I can fix it by completely un-syncing the book, then going through the above steps again (even if the box is already checked when greyed out), then re-syncing. But even after all that, sometimes it just doesn't work.
So long story short, yeah it is a very broken piece of functionality and maybe with some combinations of iTunes/iDevice doesn't ever work no matter what you do.
Also, you only need to worry about this for audiobooks that you download on your own as mp3s. I had a series of books that I listened to that way, but finished them up and now buy all audiobooks from Audible. I just do everything from the Audible app, including downloading and listening. You have to buy at audible.com but turn mp3 downloading off and then download from within the app. It's a wonderful app and has absolutely no problems saving your place! I think you may even be able to listen to mp3 audiobooks it sees in your iTunes library, try giving that a shot.
I also noticed in the app store that there's another audiobook app that lets you download and play public-domain audiobooks for free.