You only need to finish them one week. Every other week you can choose to ignore any/all of them.
This is the main point, and absolutely spot on. Assignments you don't like can be ignored once you're on the ranking board.
As for re-rolling; I guess from a personal gameplay point of view it makes sense to be able to only have assignments that you want to do, but I also feel that by signing up as a PowerPlay agent you're also agreeing to do what you're told to a point. If your power needs you to do on-foot stuff and you don't want to, well that's your choice, but you won't get an assignment bonus on your activities this week. That doesn't seem too unreasonable to me from a role-playing perspective.