The dots are just paint.
The reason they often fall out is, the installer doesn't take time to degrease the hole, and the paint doesn't adhere well.
To repair, use a solvent like lacquer thinner to degrease the hole, then dry it.
You can use model airplane paint, appliance touch-up paint, Wal-Mart hobby paint from the paint department, or even something like White-Out.
For the price and durability, model airplane paint is the best buy.
Personally, to insure a long lasting job for the customer, I used Rust-oleum gloss white paint.
I bought a small can and transfered it into some of the small model paint jars.
The gloss showed up better than the flat.
STIR THE PAINT, or you get too much solvent and it doesn't do as good a job.
Apply it with a toothpick or a small artist's paint brush.
LET DRY until BONE dry, then apply lube to prevent rust. It takes the paint longer to dry down in the hole.