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This is caused by Bezier interpretation of spatial keyframe data. There is a setting in Preferences that you can change. The ping pong motion is caused by the spatial interpretation of the velocity of the move. Your layer is moving at a certain speed between two keyframes and you decide to add another keyframe. The momentum of the layer carries it past the keyframe and then it bounces back before it continues on it's path.
If you set your preferences to display all keyframes and you select the position property you'll see Bezier handles on the path. Open the graph editor and you can clearly see the problem if you display the reference graph.
To fix the problem press the G key and hold down the Alt/Option key to change the pen tool to the convert vertex tool and click on the end of the problem causing handle and drag it toward teh keyframe or simply click the keyframe to remove the Bezier interpretation.
That's all there is to it. Change the default spatial interpretation from Bezier to Linear in the preferences and this will go away for all new keyframes but you may want to introduce Bezier interpretation manually using the pen tool on some animations.
Thank you Rick; I didn't realize that the deafault was Auto Bezier instead of Linear. I ended up ctrl-clicking on the keyframes and opening the "Keyframe Interpolation" dialogue box and changing them there; I couldn't get what you instructed to work, but that may just be because I'm still new to Adobe and don't have much experience with the pen tool.
Anyway, problem solved!