I've noticed a number of sites have mulitple DMOZ listings. Do they apply or do DMOZ decide to give multiple listings? Do I run a risk of getting my first listing banned if I apply for another listing?
Depends from case to case, I had to submit most, I think at lest one was added by editor (other then me!) on his own, it all depends how much your site is known, usually the bigger the site more links it gets, also if you have original and multilanguage content you can get more listings. Only if your first listing is in wrong category. Your site could also get moved from previous category to new one if editor decides it is more appropriate.
At the moment I'm listed in a regional category -- but there are specific services we offer that they have categories for. Should I mention in the submission that i already have a regional listing?
No need when editing it is clearly visible if site is already listed in another category but it wont hurt to leave note as to why you think you should be added to that category also.
If you tell us the URL then someone could give you better advice. Generally sites can qualify for a Regional listing and one in a topical branch. But not all sites. In addition it is possible to qualify for more depending on the content.