I am installing the pertronix II and I found this in my distributor. The vacuum advance bar has a lot of slop on the pin allowing the plate to move quite a bit. Doesn’t seem like a good place to have that much slop. How much is allowable? I suppose that once started, the vacuum  is pulling that slight advance. I marked the pin with the sloppy fit with the red arrow. 

It all adds up. What I would want to be looking at though, given the amount of wear evident there, is the overall level of mechanical wear elsewhere too - distributor cam "wobble". Excessive runout or sideplay especially makes for erratic dwell. If you've access to an ignition scope it would indicate this defect. That distributor clearly has some miles on it?

The distributor is a FEK model, so apparently that is 57-59 model year. It is not original to the car, it was on there when I bought the car, and I have no idea how many miles are on that distributor.
I don't feel any slop in the plate going sideways, everything feels tight,  although I know a scope would see what my fingers can not feel.

Those holes in the push/pull arm do become elongated. Another issue is the post on the ball bearing plate often becomes loose. Since there's no force or spring tension to hold the breaker plate stable, it will then be free to move around within the enlarged hole. The timing will be a little unstable.  If the post is supported correctly, it can be punched from the underside as an attempt to expand it in it's mounting hole. This works good if the mounting hole isn't elongated excessively.  As for the vacuum advance arm, we replaced them in the day.   These vacuum units with the straight arm as used on this style distributor have not been available for some time but someone? recently reproduced them and they are available from NPD for a little over $50. I recently purchased 2 of them and they look like a quality item.  They worked well on the distributor machine, hold vacuum and all that.  Maybe others will chime in suggesting a method of closing up the enlarged hole if the vacuum diaphragm is still good.  If this strib has a lot of use on it there are several other parts in there that wear also, like the slots in the cam base, the posts on the fly weights that register in those slots, the ball bearing breaker plate and the shaft and gushing.   Wear on all these items can stack up to produce unstable timing.  

64F100 57FAIRLANE500

I just noticed a couple new posts to this thread. Tedster is right, it sure looks like there's quite a few miles on this strib and quite a lot of crud.  At least it should be opened up, cleaned up and inspected, then go from there.

64F100 57FAIRLANE500

It appears that I now have something to do tomorrow!  I will take it apart to clean/inspect and see what I find.
Thanks to both of you for the input.