How many more "gimmicks" does adventure mode have?

I just started my second play through of adventure mode in Plants vs. Zombies, and now Crazy Dave is picking 3 (usually irrelevant) plants for me to use on each level.

After I finish this playthrough, will there be a new gimmick or handicap on further playthroughs? How many different gimmicks are there on continued playthroughs, and on which playthroughs do each occur?

After I finish this playthrough, will there be a new gimmick or handicap on further playthroughs?

No, the pick 3 is the only 'gimmick' for the adventure mode. However, a new type of zombie will also show up on the 2nd play through, so keep an eye out.