Help with my speedmaster professional moonwatch with moonphase

That is not normal for a movement in good service, but isn't unusual for one needing a service. It may just be an indication that the watch is magnetized; in rare cases this can be a sign of movement damage but chances are a standard service (which you should do anyway, having just bought it) will take care of it.

If your watch's timekleeping is fairly consistent day-to-day then you don't really have a problem. You can have a qualified technician regulate your watch's beat rate to get a daily gain or loss rate that's acceptable to you. When I bought my first watch with an 1861 movement it was losing about 10 seconds per day, which was really annoying because I hate the thought of being late for something on account of my watch. So I took it into the Omega Botique where I bought it and the technician regulated it while I watched him do it. Now I get an effective +0.2 sec/day gain, which I can control to a large degree by varying the overnight resting position of the watch.

Here's a graph of my watch's gain/loss performance plotted over time; the variations are the result of changing the nighttime resting position.

Before I give you any advice, a few questions are in order:

1 - How often do you fully wind the watch?

2 - Are these timing measurements taken with the chronograph running or stopped?

3 - What are you timing the watch against?

4 - Was the watch purchased brand new from a dealer?

5 - If the watch is not new, how long since the watch was last serviced?

Once I know these details I can give you some direction.

Cheers, Al