I had a look in my chilie book and it looks very much like it could be sun scald, or it could be a disease such as anthracnose.
One easy way to check is to see if the white spots are oriented to the sun in your garden (specifically the afternoon sun). If the white spots are on the shady side of the pod then it is unlikely to be caused by the sun. (Fungus can also grow on the sunburnt pod once its damaged). You can put up shadecloth or if they are in pots move them to a partly shaded area, or move another pot plant in to shade them.
or
Fungal infections tend to grow in humid conditions. If the problem only happens in one area of your garden check if this area is always wet and humid. You may need to cut back on the watering. Even then the plants may be diseased and a lost cause. There are fungacides you can use, I try to avoid using any chemcials on things I will be eating.
Whatever the cause I would definitely seal the affected pods in a plastic bag and bin them. Don't let any rot on the ground and don't put them in compost. As a general rule if a plant continues to produce sick pods then you should isolate it as much as possible as a first measure.
