I do not. Just ran the Android app against my site running the latest version of Role Scoper and did not note any PHP errors, even though the error 401 continues to come up for me on my Android phone.
Before I switched to Android, I had the same issues on my iPhone 3GS, and I have the same problem on my iPad 1, though the error handling is a bit different for the iOS apps. The iOS app does not show pages and offers message "couldn't sync" and "Sorry, you cannot edit pages." -- I only got an actual error code 401 on my Android. Also, Post page is empty but no message shows up.
There is some other talk about this issue at http://ios.forums.wordpress.org/topic/cant-sync-pages-comments-sorry-you-cannot-edit?replies=2#post-6784 which may help you track down the problem.
I know this started happening for me a version or two ago with Role Scoper, and that before I upgraded my plugins the mobile apps were working. It took me a little while to decide that the loss of functionality was worth investigating to this degree, so I am sorry I cannot tell you exactly which version broke my mobile app functionality. I would guess it was in the last few months.
Let me know if I can help with anything else!