I don't know if this is a real issue since I am seeing it mostly when using an emulator, but it seems to be reproducible, and I noticed it on a friend's Android device. URL is:
On some devices, particular iPad Retina emulator, when you click on the hamburger it moves the body of the page to the right as expected, but the side menu area is completely blank, despite the fact that there are elements there and you can click on them, they just are not showing up, so they are being rendered but the whole sidebar is just blank (see picture)
I did discover a useful feature on the developer menu with Safari that I was not aware of. You can go to Develop -> Simulator and use the inspector for the page that is loaded in your simulator. Quite a nice feature, but still not able to quite figure out what the issue is.
It is using a Joomla! template and looking at the source seems like it could use a lot of tweaking because there are a ton of .css and .js resources, some of which probably are not needed and some which probably conflict with one another, some which are not needed on the front end, etc.