The static being talked about is static electricity.
Until the plastic in new powder measures get coated with the graphite coating put on powder, it generates static electricity which affects how the measure works. Virtually all brands of powder measures suffer from this.
Lee usually tells the customer to run a couple pounds or so of powder through the measure to get the coating on the insides of the measure. There are some other suggestions earlier in the thread that can help with the static.
I wipe new measures down with dryer anti-static sheets and also store a sheet in the measure when not in use. It still takes a while for the static to become a non-issue. I have an old Uniflow powder measure that the reservoir is so heavily coated with graphite, you can barely see the powder level.
The static electricity can affect how the powder dispenses.
Also, when I start up a loading session, I throw twenty or thirty charges through the measure before I even start weighing charges. This settles the powder column and gets it to a uniform density.
Also, I like to use a baffle in all my drum style powder measures. It keeps a constant weight of powder column on the metering cavity. Some folks do not believe that it helps. I am not sure if the Lee Auto-drum can accept one.
Also, as said, consistent operation of the powder measure is critical to getting good results.
I find I usually get a variance of about plus/minus 0.1 grains with most powders. Some powders like Unique, the variance is a bit higher, plus/minus 0.2 grains or so.
Just a note, with handgun level charges, 0.1 grain is a larger percentage difference than in a rifle level charge.
With my firearms, I virtually always find the best charge for accuracy at some point below maximum so I do not get too concerned about the variance with the powder measure. I don't see any difference in accuracy between weighed charges or charges thrown in the powder measure.
Having said that, never under estimate the psychological factor. If you feel better about your reloads when weighing each charge, you will shoot them better.