that was the move the other skater with the other coach also had wrong.
I don't really understand - the way you described it (outside outside, inside inside) is how it's supposed to be done - you alternate feet, the 3rd circle is on top of the 2nd circle as icedancer2 said. I'd almost wonder if there wasn't something else weird going on with that one that made it not pass.
2. On the five step mohawk, I was doing a slip with one leg behind the other.
Kind of obvious but that's has never been considered a slip of any kind, that's a cross behind. Any skater who has tested these should know the pattern.. and slips show up in other patterns as well. Unless your coach hasn't at least tested through pre-juv, which would be unusual for a coach these days (many rinks require at least juvenile moves for private coaches), but even if they haven't tested it, I find it unusual that they hadn't been taught it correctly at some point in their skating career. It's even taught through basic skills in Freeskate 6.. so even if there aren't skaters taking higher tests than pre-pre and prelim I am honestly shocked that your coach doesn't know it and can't teach it correctly. It's really not a little mistake.
Honestly, that's all on the coach and if I had to deal with the embarrassment of failing because they taught me the wrong thing (which is worse than failing cause I made mistakes) I'd have fired them at the test session.
Your post sounds different when you replace "I'd learned" with "I was taught."
I agree 100% and these are issues I'd bring up with both your home club and the skating director at your rink. I don't personally feel that it's coaching behavior that should be allowed to continue without bringing it to someone's attention. If you were taught it correctly and changed it on your own or if you were taking these tests without a coach at all then that would be a different scenario, but to be taught these moves incorrectly and taken to a test session unprepared like that is completely unacceptable by a professional coach who you are paying to prepare you for a test - the fact that your coach didn't know these were incorrect and didn't seek out the advice of someone else if they were unsure about them is pretty questionable to me.