Are the specs for the "Ears of the World" challenge reasonable?
Sure it's practical, the specs sound reasonable - there's tiny FM receivers available on the market that run off small 3v button batteries. 

I think the hardest part will be designing a radio that is cost effective and can be built without a soldering iron.

It sounds like a great challenge tho, will be really interesting to see what ideas people come up with :)  

@ Cmpalmer - Do you intend to enter the competition yourself?