There are a couple of major certification bodies that test and certify professional ballroom dance teachers. In the US, the major ones are the USISTD (US branch of the Imperial Society of Teachers of Dance, a British group) and the US Terpsichore Society (but I'm not sure if it still exists). The examinations for these tests are pretty rigorous: there's a written part, an oral part, a dance demonstration part where the teacher must both lead and follow, and a part where the person being examined basically teaches a lesson to the examiner. Now, these tests aren't the ultimate factor in determining who is a good dancer and teacher and who isn't, but it is some kind of start. So see if your prospective teacher has taken the ISTD and/or Terpsichore exams. One studio I know is very proud that their teacher have passed their tests, and they hang the teacher's USISTD certificates on the wall for all to see.

Another think to look for is if your prospective teacher has ever competed as a pro with another pro partner. Pro competition is very demanding, even to the lowest-level pros, so even if the teacher didn't get very far competing as pro they still had to learn a lot and experience a lot to get where they did.

But competing as a pro also isn't a be all/end all determinant. There's some good teachers out there who haven't competed as pros. So another thing to look at is how their other students do. Dance with their students at social parties, and see if you like how they dance or not. Watch them at competitions, and see what you think of their dancing and also how they place. See if the teacher has any group classes, and take them before you start booking privates. This will give you a chance to get a taste of how the person teaches, and also to see how other students respond to what is being taught.

Some other things to look at is if your teacher teaches couples as well as single students. It's nice to work with someone who also teaches amateur couples. That way, you might get some help looking for a partner and you'll be able to use your teacher as a coach later on if you decide to do some amateur competition.

Also, look at what else your teacher does in the dance world. Does he or she stay active, taking lessons of their own? Do they participate in any dance groups, or do shows around town, or judge at competitions? It's best to work with someone who stays in contact with refinements and changes in technique, since it is always evolvoing.