In the 2+ years I've been at the Foundation a recurring email thread / bug reports have been in the form "X page doesn't render on mobile" or "Can I have a nodesktop/mobileonly class?"
The problem is almost always an issue such as a huge margin left, or some floating or fixed width css.
The answer to doing this is to provide a tool for wiki editors to allow them to fix these kinds of problems.
There is an RFC [1] open with a suggested solution, and all that is needed now is to implement it.
The general consensus was people wanted <style> tags. The original proof of concept however used a separate page (Template:Foo would have a corresponding stylesheet at Template:Foo.css) which was much easier to implement.
I truly believe implementing this would reduce the bugs raised about template specific problems, and lead to a better mobile experience. Is this something the mobile team can schedule time for, or some other team?
[1] https://www.mediawiki.org/wiki/Requests_for_comment/Allow_styling_in_templat...