PAs from the cockpit concerning abnormal situations are encouraged by the airlines. However, pilots must be very careful choosing thier words when describing some type of malfunction. Passengers will often second guess the pilots, or think that the problem is being "sugar-coated" no matter what the explanation is. I think the best way to handle the information that the passengers recieve is to keep it very, very simple. For example - an engine is running hot and the pilots are having to divert, the PA might sound like this: Ladies and gentlemen, this is the Captain speaking. We have an abnormal engine indication in the cockpit and we have decided that the best course of action would be to divert to Dallas, which is only about 50 miles away. I assure you that this is no cause for you to be concerned about, and we are landing only as a precaution. Once on the ground, our flight will be met by a representative from the airline to assist should this delay cause any inconvienence. We apologize for the unscheduled stop, but safety is our number one priority. We should be landing in a few minutes.