How to smooth out video
It sounds like the problem is probably what is known as dropped frames.  There is unfortunately not any particularly good fix.  With dropped frames, information is actually completely missing for the frames where there was no update, thus there is nothing to play during those frames.  

Depending on the length of time that is dropped, it may be possible to interpolate frames, but this is not a perfect process and will generally produce substandard results.

Basically, the idea with interpolation is that the computer tries to guess what things are the same in the frame before and the frame after the missing information and then invents frames that go in-between, but since it doesn't know what objects are, it has to make a lot of guesses and motion isn't always linear, so if it is more than a frame or two, it won't be particularly good results.

Generally, if possible, the recommendation is re-shoot rather than try to interpolate, but you can interpolate if you don't have the ability to re-shoot.  This problem also generally occurs when you have insufficient write speed to stay ahead of the video, so you may want to consider a faster memory card for future video so that you can avoid dropped frames in the future.

This question over on superuser talks about doing so with some free tools.