rpm wierdness

[HighwayUFO]

At any given speed between 15 and 25 mph, the rpms will jump from 750 to 1250. Just wondering what this is or what is causing it? The car will rock back and forth slightly during these periods. Also the car will do something similar under deceleration, almost sounds like the car will die. Please help breathe light on this potential problem.

Also, the car will hesitate on a whim. Every once and a while the car will run like a champ, and once it finally hesitates, it will continue to do so for a moderate amount of time. Feels like it is missing. Also bogs down at certain periods(mostly when hesitation occurs, but not every time when hesitating) when beginning to accelerate from a standstill Any suggestions?