Handwave: What problems dealt with and which are just handwaved is seemingly random, although handled pretty well. Nuclear plants and food are mentioned and dealt with, hospitals handwaved partially (the lack of anaesthetic may be OK for dislocated limbs, but people are going to end up with worse) and things like aeroplanes are dodged entirely (for obvious reasons).
Mary Sue: Reese. Huen even more so until he's found out.
The Woobie: Tia very, very much in one episode. And then again a couple of other times. Jeffrey also has his moments.