Both terms are commonly used. At least in the US, I think of multiracial as being a bit more formal. A lot less can go wrong saying "multiracial". Mixed is less formal, and I wouldn't use it with someone you don't know. Things having to do with race can often be very personal, so if you are referring to a specific person, don't be afraid to ask what term they prefer to describe themselves, but also try not to make it the first thing you ask about or make it seem like this is the only lens you view that person through.

In the UK multiracial is used to describe a group of people - it means that different people in the group are of different races. Mixed is a very general term - it can refer to feelings, cement, fruit etc., when referring to race we usually state it explicitly: I am of mixed race.

It depends. In my part of the US, people tend to use the term "multiracial." "Mixed" is not a preferred term. Some people will correct you if you say it (for the exact reason that Jimmy mentioned. "Mixed" can refer to things - some people think it isn't nice to use the word to refer to people.) It isn't rude, exactly, but it is less than polite.

Consider Biracial too