Is it safe to use a tea kettle with black dots on the bottom?
Those are mineral deposits. You can remove them with either vinegar or citric acid. Personally, I use citric acid:


Fill the kettle with some water.
Heat the water (doesn't need to boil).
Sprinkle a little citric acid in (use food-grade, also sometimes called "sour salt").
Let it sit for a few minutes.
The spots should vanish.
Dump the water out, rinse it a few times.


Works about the same with distilled vinegar, except you'll want some ventilation when you heat the vinegar (again, not to a boil), as the acetic acid vaporizes.

The heating isn't actually required for either approach, it just speeds the process up.