Sideways movement of the camera shows up the process by which images are captured from the chip. To fix this load the video and click on Effects> Distort.
Double-click on Warp Stabilizer to add it to the Video Effects list. This will then analyse the video track and then apply the stabilisation to it.
This also covers wobbly camera work as well, so now play the track back to check it looks okay and adjust the Smoothness and Method if necessary