Pepper plants have essentially the same needs as tomato plants, except they prefer a slightly lighter, and better-drained soil. Change your soil mix slightly to 30% sand, 30% perlite, and 40% compost. Peppers don't need as much water as tomatoes and will wilt when in need of water (try not to let them wilt). If your mix is correct it is difficult to over-water. Peppers face the same humidity-temperature problem (see above) that tomatoes experience. You will see flowers drop from the plant when pollination is unsuccessful.
The main problem with growing peppers is supporting the plant. You need a light, sandy soil to grow them well, and this type of soil provides little support for the root structure. Plants will tip over once the peppers form if not well supported. Once a plant has tipped over it will never be a producer.
We have found that three 5-foot stakes, driven 2 feet deep, work best to support a large pepper plant. Try the velcro ties, they seem to work very well.
Once you start to see small peppers on the upper portion of the two (or three) branches, it is time to place stakes to support each of these branches. Place these new stakes 6-12" on either side of the main stake, and tie the branches to the new stakes.