Thanks you guys, for all your help here. I'm gonna do the trans fluid and filter next, even though the lady I just bought the car from said the trans was recently "rebuilt".
That could well be, but it reminds me of a guy who used to live next to the cycle shop I worked at, who sold "rebuilt" car engines. He always had people looking for him a day or two after they had picked up their freshly overhauled engines, and so after some investigation I found out his game: he would get a motor from the junkyard, sandblast it and put on a fresh coat of paint, then advertise as rebuilt!!! What a scam artist, boy, they sure LOOKED good.
So I will take your good advice on servicing the tranny before anything else, then check the other things mentioned as well.
Thanks again!
Mike