Thanks for the reply,nvestysly. Actually, the more I looked at it, the seal at the top is held in place on the door in a grove, so I wouldn't expect to put any adhesive in the top part of the door. And the bottom of the door is held in place by the clips, so maybe it only needs adhesive on both sides of the door jam. Then I took a look at the other (good) door, and it has adhesive all the way around the door. I got a reply back from the wholesaler who sold me the weatherstripping, and they said use adhesive all the way around the entire door. Yeah, you're right about the 3M stuff...it can be nasty.
With the way you did it, did you ever have any problem with leaking around the door?