No, it is not dangerous, and it is easy to fix the exposed area so as to avoid it rusting.
Samuel M. Goldwasser has written a great article on microwave ovens which has some great tips on your problem and how to repair it.
Here is the pertinent excerpt.
Notes on the Troubleshooting and Repair of Microwave Ovens
"Use fine sandpaper to completely smooth out the metal and feather the edges of the paint in the immediate area. Until you can obtain paint, the oven will work fine but since the chamber is made of sheet steel, rust will set in eventually. So, do paint it.
Special microwave oven cavity paint is available but any common gloss enamel will work just as well (and costs about 1/10th as much). Unplug the oven as paint solvent is generally flammable. Use touch-up paint with a small brush (recommended) or spray paint (be careful to mask off all but the immediate area). Allow at least 24 hours to dry with the microwave oven door OPEN so all the solvent has evaporatedf. The typical color is beige, almond, or some other form of off-white - just match it to your oven (if you care). While I have never heard of problems caused by these non-approved paints, it's always a good idea to test first in an inconspicuous location to be sure there are no surprises when power is applied. Test by putting a cup of water in as a load and running for a minute or so on HIGH. The area where the new paint has been applied should not be any warmer than other areas. Of course, there should be no smoke or six foot flames. :) But the odor from petro-chemical solvent-based paints may linger for some time and could be quite objectionable in the vicinity of food. Once the paint is dry to the touch, a blow-dryer on low heat (NOT a heat gun!) applied to the newly painted areas may be used to speed this along. Running the oven on the lowest setting should help as well, as the fan will circulate air throughout. Make sure there is a water or other load in the oven when doing this! Also, putting a container of used coffee grounds in the oven overnight for several nights should help clear the odor.
As noted, damaged paint is often a symptom of other problems, most likely due to debris causing hot spots. If around the waveguide cover, there may be gummed up food trapped under the cover. If it occurred along the turntable track, the turntable wheels themselves may be full of carbonized food causing heating and/or arcing as they rotate on the bottom paint. Any of this will destroy the new paint if not thoroughly cleaned first."
