I've just been visiting math.stackexchange.com where they use a range of shapes to signify badge class as well as colour.
This makes the differences much easier to see and is generally more accessible - Should UXSE be doing the same?
Yes, although a minor point I would probably agree. It's less of an issue for people with all three classes of badge because the order of the badges is always consistent (the same way that traffic lights aren't set in different shapes - we know the bottom one is always the green one), but in Stack Exchange world people can have one, two or all three types.
Due to the presence of the reversal and populist badges, it is possible to get a Gold badge without actually having a Silver one first. Therefore just because someone has two badge classes that doesn't mean it's definitely a bronze and a silver.
Minor UX stuff this, but that's what we in the UX world love - the little details!