Crap sorry, I was thinking the minute recorder was not resetting to "12". May still be a simple matter of resetting the hand, but then the minute jump will be off, which means moving the finger on the chrono runner. What I actually suspect is that the hammer is out of adjustment, and is making full contact with the minute counter but not the chrono runner, and you want the reverse of that. Depending on the version you have it may have an adjustable hammer, or may require filing.
The dial looks good for it's age.
From my experience there is really much that can be done to improve the look of a vintage dial. Often what appears to be dirt is instead oxidation and cannot be removed without changing the appearance of the dial. I would stick to using Rodico and Q-Tips dipped in distilled water. If you do anything, be very careful and work very slow. Keep in mind the printing on the dial is often placed on top of the lacquer and it's the first to go when "cleaning" is attempted.
Thanks. That was going to be my first step. I asked because I was curious if the "resets wrong but advances right" was indicative of something specific that I haven't come across in discussions yet.
Worst case scenario, I line up the second hand and don't think about it much when the minute recorder advances.
I think you can just remove the hand and set it at zero when in reset position. If that doesn't do it there's a laundry list of potential issues, on which books have been written. Try that and if you still have a problem it can be addressed.