I think there definitely needs to be an admin selection of "finalists."
What to do with the finalists is the next step. Here's my idea:
Have the previous contest's winners vote on the current contest's finalists. That way the prizes get spread around and new artists are featured. When you win a contest, and then vote on the next contest, you're free to enter the contest immediately following the one you voted on. Sure, you can always create alt accounts and try to vote AND win, but all admin has to do is keep track of mailing addresses for a month to prevent that.
Have the panelists' votes based on a 1-5 scale for each of the following: originality, technical merit, theme appropriateness, humor. I also think each member of the voting panel should write a short review for each entry to accompany/justify their score. They should also help decide the topic for the next contest. Oh, and have a guest judge thrown in there every so often to spice things up.
The main rationale behind this approach is that the art submissions should be judged by qualified artists to prevent it from becoming a popularity contest & dominated by 13 yr old doofuses.