Well, it's been so long since I had a date, or even had a guy flirt with me, I'm not sure I remember anything about it--BUT:
1. Paying her back. If you were going to do this, it needed to be the VERY next day. By now, that train has left the station. On the other hand--did you TELL her you'd pay her back? If so, then DO it. It'll be awkward, and it won't make things a bit better, but if you SAID you'd pay her back, you gotta follow through.
2. I agree with Derrel about the lack of leadership you showed on the date. You had no cash--sure, you expected to use your card, but ALWAYS have a backup plan! Second, she drove--do you not own a car? Third, you were late to the movie--were you just not paying attention to the time? And fourth, and possibly most important: I suspect that, when the incident happened with the card, YOU, feeling bad about it, contributed *greatly* to the rest of the night being awkward.
So, let me give a tip: HUMOR goes a VERY, VERY long way to defuse an awkward situation. I'm not saying laugh it off and act like it was no big deal, but DO take it in stride.
3. RELAX! Don't sweat the small stuff.
If you really like this girl, and want a chance with her--just take it slow, but don't allow yourself to be relegated to the Friendzone (so THAT's what they call it these days, huh?). Send her a card just to say you're thinking of her. Leave a bouquet of flowers and some chocolate at her door--just find little romantic-but-not-overly-so gestures to say that you are interested in her as more than a friend. Then she will either warm up and go out with you again, or she won't. If she won't--well, why would YOU want a girl who isn't interested in YOU?
My oldest son tends to make his "girl of my dreams" choices based on one criteria: She seems to like me. But as I've told him over and over, if SHE does not see great value in WHO YOU ARE, then she is not right for you.
Sounds to me like this girl, so far, is missing the value of YOU. Find someone who will value you.