why did my record player slow down, speed up, then go back to normal?

Happened to me with my older Luxman PD-277.  There are speed control potentiometers for 45 and 33 RPM and they were showing their age.  A little DeOxit cleaned them up.  The wiper contact was a little dirty.

atmosphere is correct. The speed potentiometer might be corroded. This happens a lot on old technics 1200 tt. It's also could be the speed control module. 

If it’s a belt drive, the belt may be stretched or worn. Could be a dirty speed control potentiometer! If it’s direct drive, could be a problem in the servo drive ckt. 

Good lord. Love to see the usual suspects as the first ones chiming in with snark and nothing to add. 

Now after a full day of denial the military has released evidence of multiple sightings by pilots and radar. What was originally denied to even be happening is now openly discussed as being due to space aliens. Unfortunately too late, as we can see from the lack of replies the OP has been abducted. If only he had known to unleash the yodeling. https://youtu.be/aTe0MjAZvMU?t=49