Look at the situations you are in from a longer term, are you going to marry this guy? You don't know yet, that would take quite a bit more time to know. So, while you are learning more about him and he, about you, enjoy the process.

Currently you are going to see movies with a coworker you enjoy. You do not have to worry about whether he wants to kiss you until you are alone and he acts like he wants to kiss you. You do not have to worry about what other people will say about you hanging around with him, as you say, you're only going to a movie! When your mind starts to try and panic, remember where you are and that whatever is scary is not happening yet!

I would start a little journal, as if you are doing a homework assignment on "dating" and I'd sit after each time out with the guy and write down everything that happened, that you felt and thought, etc. Knowing that you are keeping this "journal", perhaps the worse symptoms of anxiety will wait and/or look forward to getting beyond the date to the journal? It is like a scary dream when you are recording your dreams, it becomes interesting, looking at the symbols instead of the fear/scariness being your focus; make the process of dating this guy and what you are "learning" the focus instead of the individual, scary parts being so.