The number one mistake I see made by those new to D/s is thinking there is a right and a wrong way to go about playing. While there are some safety rules that should be followed, the only people who make the rules are the ones involved in the scene or relationship. If anyone else tells you that you are doing this wrong, tell them to mind their own business.
Another common mistake is rushing into things. I know that after years and years of suppressing this desire it is very hard to take it slow when you finally find out you aren't the only one that gets turned on by bondage. But rushing to dominate or submit to another without taking the time to get to know some skills, and each other, is a recipe for pain... that is the bad kind, not the good. When you first get started, take the time to read the literature, join a local organization, and get to know the person you will be playing with.
A mistake I often see new subs make is submitting to anyone and everyone who calls themselves a dominant. Just because someone sticks "Master", "Mistress", "Dom" or "Domme" in their screen name doesn't mean you have to call them "sir" or "ma'am" or submit to their demands. For the most part, a reputable, experienced dominant knows this and will not demand unearned respect. New dominants are sometimes guilty of this. If someone hasn't earned your respect, why would you act like they have?
Another mistake inexperienced subs often make is in setting limits. Some make too many limits, and this will sometimes frustrate or scare off the dominant. Much more common is a new sub setting too few limits. They feel they will not be desirable or "sub" enough if they have limits. Take some time to think about what truly squicks you... what you do not under any circumstances want to experience at present, and make this act a limit. If a potential Dom/me won't agree to a certain limit, walk away. Of course, your limits will change as you become more experienced. What you won't submit to this year, you may crave the next.
Something else I have seen is the "Dom/me is always right" syndrome. The joke is there are two rules in D/s:
The Dom/me is always right
If the Dom/me is wrong, refer to Rule #1
That's what it is, too... just a joke. Dom/mes are human and are sometimes wrong. It isn't a sin against the D/s gods to respectfully suggest to your Dom/me that s/he may be wrong... especially if it involves a safety issue. Just because you are a sub doesn't mean you check your brain at the door. If you are the dominant and make a mistake, don't be afraid to admit it and apologize. It won't make you any less "domly".
Finally, many newbies think that the Dom/me's pleasure is the only thing that matters. Sure, as a sub it is your job to please your Dom/me, but it should please you as a sub, also. We play these games to make everyone happy. While there may be times you do something to please your Dom/me that you don't enjoy, if you find yourself doing this consistently you are probably with the wrong partners.