A new LMS accessibility study from University of Illinois was published recently, unfortunately they had Moodle 2.3 only, but has some useful things to say:
The main issue they had was unfortunately with our filepicker, which is complex.
I've created this issue to address that. The FRONTEND team needs to develop a list of the exact problems (as subtasks here) and then tackle them together.
Note that it's likely that accessibility improvements will also make the experience better for everyone on touch screens.