Hi Glen,
Wow and 8 feet tall Mugo must be a sight to see - and you have two of them!
I believe the brown wormlike structures on your Mugo are the male flowers. Although it doesn't look exactly like the image shown in South Carolina extension website it does says that there are male and female cones parts.
 "This shrub produces inconspicuous male and female pollen cones from May to July. The male pollen cone is greenish-yellow and 0.25 inches long. The female cone ripens in the fall and becomes oval to conical, sessile, 1 to 2.5 inches long, and dark brown."
Pinus mugo (Mugho Pine, Mugo Pine, Swiss Mountain Pine) | North Carolina Extension Gardener Plant Toolbox (ncsu.edu)
While not research base, if you look up "mugo pinus male flowers" you will find images similar to your picture. I hope this alleviate any concerns.

The white spots could have been Pine Needle Scale. Treatment with a horticultural oil (like Neem) is appropriate although scales have a waxy covering that prevents complete eradication and there may be eggs in waiting ready to hatch. You should be vigilant in your monitoring is case more treatment is needed.
Pine needle scale (missouribotanicalgarden.org)

I hope your Mugos continue to give years of enjoyment.

---