One problem related to automatic transmission control module has been reported for the 2001 Saturn LS. The most recently reported issues are listed below.
I own an 2001 Saturn l-33, with 38,280 miles. On two occasions the service light (not the service engine light came on, and when this occurred, the transmission would shift harshly. On 04-30- 2009, I had started the car, which had no been used that day, I was sitting somewhat sideways in the drivers seat talking to my father, when the auto when the auto went into reverse by itself, and dragged me across the street, hitting a block wall. I got up and into the auto, and noticed the shift lever was still in "park". I found a websight "the Saturn forum" wherein other Saturn l-300 owners had the same problem with the service light coming on etc. As far as I know, Saturn has not sent out a service bulletin, or re-call on this problem. I also found out the problem might be due to "pinched" wiring going to the "transmission control module. I am hesitant in taking the auto to the dealer for repair as I was injured, and I might re-tain legal council in this matter. I think Saturn should be notifying people of the possible hazard involved in this auto.