Problems & Pests:

Diseases are not that common on chilli peppers, but here are the main culprits, the main thing is to catch them early, over wintering a plant will need careful monitoring in the Autumn especially bringing it in into a warmer climate.
Damping Off: Most seedlings are potentially susceptible to this, fungus attack on the new thin stems fairly close to the base, weakening and thinning of stem and then plant collapses, not much can be done although there are treatments to water in before it happens but generally it is time to dispose of plant. Always plant in clean trays with good compost and clean water to start, a watering of a copper fungicide may also help prevent attack.
Slugs & Snails: Like fresh new growth to snack on, some damage can be limited by watering in the morning as slugs are most active at night and are most efficient in damp conditions. They also dislike venturing over rough and sharp ground such as shingle, sharp sand or even fine wood mulch, coffee grains also act as a deterrent. Seaweed if available puts them off with the salt content, so a mulching of this may well help, or try a beer trap as they are quite partial to a bevvy. Set a small amount of beer in a shallow wide jar buried in the soil up to its neck, slugs will crawl in and drown, as they are attracted to the yeast and barley in the beer.