Can anybody name all the problems and adventures that have taken place with Jerry's infamous car?

Good question Elaine. I guess there were different versions of the car. Let's see, it got destroyed at the Puerto Rican parade.

132/132 The Bottle Depost 1&2:
It got "stolen" by obsessive mechanic Tony & chased by Kramer driving Newmy's mail truck & used to launch golf clubs from.
& Jer almost thought it was totaly destroyed but that one ended up being some other gal's turbo model. Her's was midnight blue but I'm not sure what color Jer's was in this ep.

In 167 The Dealership Kramer & salesman "Rick" run out of gas in a new black 9000 Jer was shopping for.

In 150 The Pothole 'Lainie uses it to haul a bunch of garbage to the dump (she's playing janitor in her building to use the janitor closet to order food).
And then she does some of her spooky driving in it as she uses the wide lanes of Kramer's custom section of the Arthur Berkhardt Expressway with the garbage flying out the trunk.

George runs over a pothole and the car starts to make a clanking noise in The Parking Space.

Kramer and Newman put their groceries under the hood in one episode. I think it was the bottle deposits.