The long-term accuracy of the grid frequency is very high. You'll remember the old ac clocks that used a synchronous motor would almost always keep perfect time. Over the short term you'll see some variation, but nothing like the one percent error your meter is showing.
Back in 2011, the power companies experimented with letting the frequency drift a bit and not correcting it over the long term. I googled and found a few old articles about the experiment, but nothing about the RESULTS. So I don't know if they decided go back to the old rigorous regulation or to allow frequency variation to continue.
I think the real problem with your meter is noise. It's not easy to make a cheap, accurate, broad-band frequency meter. (If you try comparing different cheap guitar tuners, you'll quickly find they are not at all the same.) A little noise is going to introduce some extra zero crossings that will really trash the measurement. You might try adding a low-pass RC filter to your meter and see if that improves the measurement. Also, is there a spec for your meter's accuracy? If the manufacturer doesn't publish the accuracy, it's fair to assume that one percent is about all you'll get.
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Today's Featured Article - Show Coverage: Journey to Ankeny - by Cindy Ladage. We left Illinois on the first day of July and headed north and west for Ankeny, Iowa. Minus two kids, we traveled light with only the youngest in tow. As long as a pool was at the end of our destination she was easy to please unlike the other two who have a multitude of requirements to travel with mom and dad. Amana Colonies served as a respite where we ate a family style lunch that sustained us with more food than could reasonably fit into our ample physiques. The show at Ankeny
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