Thank you for your question.

I'm sorry to say this looks like magnolia scale, which is a widespread problem in our area and particularly with a few popular varieties including star magnolia. In other years, heavy wind and more frequent rains have helped knock these pests off plants, so our drought last year and this year may be contributing to a wider prevalence of scale.

Scale is an insect that sucks tree sap and excretes large amounts of honeydew. Just like it sounds, honeydew is a sweet waste substance that sticks whatever it lands on; the sugar it contains attract ants and wasps. The honeydew can be a breeding ground for sooty mold fungi, which would explain leaves or branches you may have seen that look like they've got soot on them.

Magnolia scale can cause slow growth and, on trees that are heavily infested, substantial weakening of branches, branch dieback, and eventual tree death. 

The white spots you see right now are nymphs that hatched from eggs laid in June. The nymphs will soon become young mobile crawlers, and then they will overwinter and reach reproductive maturity in the spring.  

Right now is the time to try mechanical control, especially since that white waxy substance coating the nymphs will make them impervious to pesticide. You can pick the scale off and just throw them on the ground (they won't have a way to get back to the tree and will quickly die). You can also try blasting them off with water (read about how the Minnesota Landscape Arboretum does that).

Later in August, the nymphs will emerge from that white waxy coating as young, mobile crawlers and will remain in that stage until winter. When nymphs are in the young crawler stage, you can use a combination mechanical-chemical control by applying horticultural oil. (You can read about oils here.) At the landscape arboretum, they're applying horticultural oil in both the fall and the spring.

I hope this is helpful, and wish you success in removing the scale from your tree!