How can one find out if a martial art school is legitimate/registered? I took a style back in the 90's called Chung Moo Quan. The school eventually closed because of some investigations into it being a cult and the master, John C. Kim, went to jail for tax fraud for 5 years, I think.
So basically, did I waste my time on a martial art that was just a school that took peoples' money and wasn't even legal?
There are a few different phenomena that are easy to conflate here and which may or may not impact the perception of "legitimacy."
One are claims of lineage. A lot of martial arts, especially eastern ones, have a variety of extraordinary claims about their lineage that are a) largely irrelevant and b) pretty grandiose. Frequently conflated with cultural meaning and conflicts that people in the United States are usually only vaguely aware of (e.g., it used to be said that the founder of Hapkido "lived in the mountains" and came down after World War II, partly to avoid saying that he had actually been in Japan).
Related to that is the matter of registration and certification. Sometimes the registering organization can give you an indication, but I've known some very good instructors who have no (advertised) official affiliations along these lines, or who have certifications that it is very difficult to confirm (e.g., it requires being able to speak Korean to actually confirm what they are saying). The latter is a solvable problem to some extent, but not a trivial one. On the other hand, I've known some very bad instructors who have a long list of things posted on their wall.
For example: You'd find no certifying organization for my rapier school beyond that they met a certain minimum of safety standards, but they were still quite excellent and dedicated to the art, and had some great students.
For a movie reference, compare the characters of Mr. Han and Master Li in the 2010 edition of the Karate (Kung Fu) Kid (or John Kreese and Mr. Miyagi in the original).
Another item you'll come across is that many martial arts schools have a tendency to try and talk themselves up relative to their competitors. Practitioners will frequently make claims that just aren't true, or the differences may be true but it is debatable whether the form is superior–or even significantly different–on the basis of those claims.
How much this matters to you is, well, up to you and it also depends on what you are looking for as well as what you personally believe. In many cases in the United States, at least, these are now toned down or not made with the same force that they used to be, but you'll still find remnants of these claims drifting around. You'll also still find plenty of talk about concepts that are not well demonstrated by evidence-based scientific process. This, again, mostly depends on you to the extent that you will want to worry about it. Some very good martial arts instructors still have some claims built-in to their arts in these regards and it doesn't really detract significantly. In other cases it can be a significant hinderance to learning what works or doesn't from a martial art.
As a general rule, many martial arts are "effective." The question is "at what," and that depends on your goals more than anything.
While I'd argue that the earlier two categories are frequently conflated with legitimacy, I'd also argue that by themselves it doesn't tell you much one way or the other. These martial arts are going to be–by and large–legal, regardless of whether they are effective. Kim's schools were eventually broken for things relating to false advertising and tax fraud, but it would have been very difficult to ascertain the extent to which the books were cooked just by being in the classroom.
Instead, go talk to the students and the instructor. Watch them work. Don't just listen to their marketing material, but actually have a conversation with them. Look at the conversation in What Martial Art Should I Start With? as a baseline here. See what you have fun with. See if you can find statements about them online (a lack of statements is not necessarily a danger symbol: some of the best instructors I've seen have very little presence, but if people are making lots of negative statements you should at least listen). See if they are the sorts of people you want to hang around with.
Some things to look out for:
At the end, the most important questions are: "Can I learn here?" and "Is this what I want to be doing?" Even an art that is not run very well may still be effective for you, while one that is run extremely well you may just not click with for one reason or another.
David has an excellent answer.
I would just like to add that it is important to remember that styles evolve over time - this is a natural phenomena that has been going on for centuries. It is a result of students getting to a sufficient level where they start their own school, they then have their own style of teaching and will tend to emphasize the parts of the style that they prefer or have found to work for them, and they also tend to mix in teachings from other arts they may have done. There is nothing wrong with this and it doesn't mean the style or instructor should be avoided.
You could stick to a school that has a proven lineage back to a governing body, but that by itself doesn't make it a good choice. It means you will get taught in a franchise or cookie-cutter fashion, your progression and learning can be predicted well ahead of time, and if that is what you are happy with then more power to you. The instructor's capabilities are more important than the school's lineage or (stylistic) political affiliations.
None of us like it if we pay money for something and don't receive good value on that money. Your previous instructor going to jail for tax evasion doesn't make the style illegal, it simply means he didn't run it as a business in a way that complied with goverment regulations. It doesn't necessarily mean what he taught you was a waste of time - you should have something that you can take away with you and apply in the next style you learn. One thing you can certainly take away with you is knowing the warning signs of a school that is being run in an unmaintainable way so you won't get burnt again.
