From here:
http://msdn.microsoft.com/en-us/library/live/hh826531.aspx
Looks like a variety of filtering and selection mechanisms. Not one explicitly for mime-types but it does let you filter on some notion of 'type':
Get only certain types of items by using the filter parameter in the preceding code and specifying the item type: all (default), photos, videos, audio, folders, or albums. For example, to get only photos, use FOLDER_ID/files?filter=photos.
Also looks like you can sort by a variety of criteria and then select by offset, which would seemingly be very useful for what you discuss above.