Finding mail problems

Dear all, I would appreciate any help in finding the best places to look when there are complaints about people missing messages on lists that I manage. I've turned on verbose logging on one of the lists, but there's no sign of it being unable to send messages to any of the people. I've sent a test message and asked people to reply to me if they receive it, so that I can get some idea of who isn't getting messages. The problem addresses seem to vary, judging by what people are saying - they receive some messages but not others. Any clues gratefully received. Many thanks, 'ö-Dzin Tridral