A few months ago the digital dash started going haywire, where it would say l was going 0mph when l was going 50, or it would jump from 20 to 75 to 3mph on the dash when l was going 50, for example. A little bit after this started happening, the transmission would sporadically shift as if it was trying to keep up with these speeds being displayed. On top of this, the car would feel very sluggish whenever the speedometer did this. This did not happen all too often however. Flash forward to now and the speedometer reads 0mph 95% of the time I am driving, the car shifts sporadically very very often (example: on the interstate, driving 75 mph, the car will downshift 1 or 2 gears and redline at 6k rpm, then l have to wait for what seems to be the gear to catch and shift into the proper gear, and then l can accelerate again), and it still has the sluggishness. Is this mechanical, ecu, tranny (l know these cars are notorious for bad trannys)? Is it a mixture of these problems? Something else?

Well harware wise the tranny IS working so l would say no to the transmission and yes to the electrical. It (in my mind) has to be something like a sensor that detects speed and the transmission must respond to that.

Your vehicle speed sensor is bad. It goes in the tail shaft of the tranny (farthest end from the engine normally) and tells the computer how fast you're going so that the car shifts properly. The sensor is easy to change and costs between $20-$40. It goes where the speedo cable would go on an older car if you know where that is.

Is your car a 2 door also? The Sable does not come with a 3.8L engine, only a 3.0L unless the engine has been changed.

First off check the ground on ur battery. My wife is 96 Sable had a cracked battery & allowed acid to collect on the negative cable & corrode. She started complaining that occasionally the headlights would flicker & the engine would start to die then catch itself only to rev up & the car would take off. Bad situation if u were in heavy traffic. She said the couple times it did this the clock was reset to 12:00 & the stations on the radio were all reset from their presets. Which told me it was losing power, then regaining it.
That is when l checked around under the hood, there was a small crack in the battery right beside the negative post. The cable was terribly corroded. l replaced the battery in my case & soaked the cable ends in baking soda water, til they stopped fizzing then hooked the battery up. That was 3 months ago & she has not had a problem since.

My guess is that when the battery lost ground, it was disconnecting the computer which upon reconnection enguaged the cruise control that tried to accelorate the car out of control. l am only trying to help u do a cheap trouble shoot, not that l am right or anyone else is wrong. Hope u find a good solution.

Since the engine computer does not know how fast u r going.. (0 mph is the hint).. the transmission will guess when to shift by other ways & u get all the weird sluginess & such u r feeling right now.

The digital dash is related to the same thing affecting the transmission.. My guess is either the check engine light is on, or a code is stored in there for a VSS issue

As someone else said, it is probably the VSS on the right rear of the transmission near the right cv shaft. If u r not a advanced level shade tree or better, best to leave to the pros. Have seen the sensor go out, & have seen the wires get damaged also.. but both will cause the problem u have.