For me the most exciting prospect of the JWST is the ability to analyse the spectra of atmospheres around exoplanets. We could have tantalising evidence of extrasolar life in just a few years.
I'd really like to know the story behind how they got a V2 rocket out to White Sands and actually conducted this flight. It has to be a fascinating story - one I hadn't even heard of until now. I assume this was broadly part of Operation Paperclip, and either fully assembled rockets or their components were moved out of Germany and to the United States at some point.
Edit: I take it back, the wiki does link the final project report from 1952 that goes into detail about how this was accomplished. It's worth reading.