I have the same problem, even though I have several Burmese Unicode fonts installed.  I suspect that Burmese just has poor OS support.  You can fix it by going to the left of your screen, down below the search bar, under 'languages' where the interwiki links are.  You should see a gear by 'languages'.  Click on it to get your WP language settings, go to the fonts tab, and check the box for 'Download fonts when needed'.  Why this works when you already have the fonts you need, I don't know.  You should now be able to see Burmese, but headers or other languages may get screwed up, so you'll need to play with it to see what works for you.  This was intended to be rolled out as the default interface, but it's still too buggy.  —