I noticed my beater watch was running a bit erratically so I put it away to await repair. I finally got some time to take a look at it today and its cause and solution were very simple and I figured worth a post.
When I put it on my timegrapher a pattern was apparent; about once per minute its amplitude would drop dramatically causing a proportionate increase in its rate. Because this was occurring with the frequency of once per minute and with good regularity I thought I should begin troubleshooting the part that makes a revolution at the same frequency: the second hand and the fourth wheel and pinion which it rests.
It it wise to observe first and look for the obvious so I began by watching the second hand sweep around the dial while observing the amplitude reading on my timegrapher. Sure enough, the change in amplitude occurred every time the second hand passed by the minute hand. I adjusted the fit of the hands and, voila, the problem was solved!