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

Depending on time of day and prevailing weather conditions driving load against the power grid, it might have been a fluctuation in available current in the power grid feeding electric service to your home. It happens on a weekly basis for our power grid. The various fans that help our ancient HVAC system move air in our home will slow then speed up at various times through the day, much too subtle to cause the lights to dim. Once the load stabilizes after 10pm or so all things plugged in are much happier. 

And you think that's all it is then. Interesting.
https://www.youtube.com/watch?v=G554Xa8MElg

hey guys. thanks for all the responses! it is a belt drive, and i was about 25 minutes into one side of a record (CSNY's 4 way street, side 3, southern man, in case anyone wants to know). It was kind of a humid day. This has only happened once.

thanks again everyone. any input helps.

@stereo5 thanks for the tip! i'm going to do that, even if the belt isn't the problem. (it probably is, but then again, it only happened once for about 30 seconds.)

@atmasphere thanks. this is an older turntable, but it has electronic speed buttons (33, 45 rpm). I think i'll check the buttons for corrosion.