American Waltham movement, 18 size W. Ellery 1857 model.
It was made about 1873.
A cannon pinion being too loose is a common problem in vintage watches. The cannon pinion sits fiction-fit on the center shaft. It need to be loose enough to slip when the time is being set. But it also must be tight enough to grip the center staff and turn as the watch runs.
When the cannon pinion is too loose, it slips and the hands do not move even though the watch is ticking away just fine, and the center wheel is turning. The fix for this problem is to tighten the cannon pinion, in most cases. Later cannon pinions, later than this one, are built with a cut-out in the side, like a flap, that can be press in some to tighten the grip. But this old key-set cannon pinion is solid. It can not be tightened in the usual manner. There are a few tricks to work around this, none of them advised. The watchmakers of old would have been trained to replace the part if it was too loose. The problem might actually be wear to the center staff, which perhaps should be replaced.
Some prior watchmaker has filed down the wall of the cannon pinion until it was thin enough that it could be indented in with a punch. It then grips the center tightly at that point.
We have to accept in this day and age that this may be the best that can be done. But it is problematic. First, it is tricky to do. Remove too much material and the part is ruined. Secondly, and more importantly, it will not last. This dimple inside the part is not like the spring-like flap later designs use. The fix here, in actual use where the watch is set every day, would quickly wear down and go right back to slipping, and likely cut a groove in the center shaft too, damaging that part.
But this is an antique after all, and should see very infrequent setting.
Setting a watch like this has to be done with great care, as it is very easy to slip and damage the hands.