Good dojo:
*Ditto to the above note about "free lesson" or three. You want to make sure you're comfy there before you start investing a lot of money in it. The sensei or teacher and the other students should
want you to be there and to feel comfortable.
*Doors are open to everyone. If a paraplegic wheels in and says "I want to learn martial arts," she is welcomed with glee.
*The classes are broken up by age and ability so that everyone gets time learning at their skill level, BUT all ages and abilities are welcome to spar with one another for practice. In a good dojo, the better students will want to help those who aren't as good to progress. (There is a contact system taught to ensure no one gets hurt, and there is an agreed "release" signal if something starts hurting... usually "tapping out.")
*Some competition among students exists, but sensei or teacher doesn't favor the winners over the losers or vice versa.
*There is discipline in the dojo, but there's room for humor too. Flexible bodies, flexible minds.
*The sensei or teacher should have at least a black belt, preferably in more than one form.
*The sensei or teacher gives you lessons in philosophy as much as s/he gives you lessons in fighting, if not more. S/he will speak of her/his sensei with great respect.
*Other fighting systems, meditation, yogas, gymnatics, and other physical disciplines are valued.
*You'll usually sense a centeredness in the sensei or teacher and in the experienced students. It's hard to explain, but these people exude a quiet, but (unless they are sparring or involved in a formal competition for titiles) humble dignity and confidence.
*Criticism is given with explicit instuction on how to improve what you're doing wrong, usually manually or physically, at the time the criticism is delivered.
*"You need to practice more" is heard continually. "Very good, but do this slightly different" is heard quite a lot. "That's perfect" is almost never heard. "That sucks, only seppuku will save you." is never heard... in a serious way.
*After about a month, you feel very safe and comfortable socially, even if you're physically clumsy.
Bad Dojo:
*People are mean to one another, in-fighting develops.
*New students or those of lesser ability are picked on.
*The teacher is focused on fighting, not on developing mind.
*You feel uncomfortable... for whatever reason.
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p.s. I'm not an expert, like you wanted to ask. I've only done karate since 99.