I don't have much regular butter on hand to make a roux. Is it a good idea to use clarified butter instead? What could go wrong?
Most chefs use clarified butter for almost everything. It is never in recipes probably because it is not common in home kitchens and a lot more expensive. Easy to make your own and then you can store in fridge for a week. Restaurant kitchens usually make a bowl for the day and then have it next to the stove where it stays liquid and easy to use.
Different types of sauce of course need different type of butter. Generally clarified butter can be used in any sauce that is using butter as a thickener; all cream (or God forbid milk) sauces made with standard butter as there would be milk protein anyway; emulsions with egg yolk are in fact better with clarified butter. The exception would be "beurre blanc": as it is a butter sauce with no other emulsifier, it uses the non-fat milk protein to help the emulsion stay together.
Happy cooking and enjoy the taste!
Making your roux with clarified butter will certainly work, and work well. Clarifiying removes the milk solids, which add nutty flavor when browned. Without them, the roux would be far less likely to burn, particularly if you want a lighter roux. Whether you're going for white, blond, brown, or dark brown roux, using clarified butter should not present a problem.
Your roux will actually be easier to cook out (getting rid of that flour-y taste) if you use clarified butter, so you can cook a very very light roux that doesn't taste like a dough ball. When I have time for the extra step, that's how I make bechamel. If my kids sniff even a trace of flour in their cheese sauce I'll be left to eat a whole lot of mac-n-cheese alone.
Now, it doesn't make sense to use clarified butter with flour with a beurre manié even if it seems like essentially the same thing. You generally finish a sauce with that to thicken it and give it that lovely sheen, and that (especially the latter) works best with whole butter, in addition to being quite a bit easier to handle.
I haven't tried using clarified butter with a beurre blanc, though. I suspect it'd work in a pinch if that's all you had, but it wouldn't occur to me to try it deliberately since it's a little odd to work to remove milk fat just to end up putting a whole lot more back in :)