I like this idea. It could be good fodder for Dave's YouTube channel. Prizes could be simple stuff like a monthly uCurrent, shirt, or even some of the mail-bag like flair that people send in for him to show off on the blog (widget they just started selling, kickstarter promo, etc.).
Monthly could be fundamental novelty circuits in the spirit of open source. Pulse generators, audio amplifiers, discrete versions of common chips (i.e. 555), etc. Maybe an open-ended yearly contest of a larger system.
Just throwing out thoughts.