There are any number of moral messages in The Strange Case of Dr. Jekyll and Mr. Hyde, but one of the most prominent is that we shouldn't take people at face value. As always, it's their moral character, not their outward appearance that really matters.
Take Dr. Jekyll, for example. On the outside, he's the very epitome of respectability; an educated, socially-prominent man, he's the last person anyone would suspect of carrying out such foul, wicked deeds. But therein lies the problem. People attach so much importance to outward appearance that they don't realize what may be going on beneath the prim and proper exterior of the social elite.
An additional moral message to consider is that one shouldn't suppress one's inner emotions as so many people in Victorian England did. If one were a psychoanalyst, one might argue that Mr. Hyde is the inevitable result, the hideous by-product, of Dr. Jekyll's chronic inability to deal with the myriad disturbances buried deep within his subconscious. Dr. Jekyll is unwilling or unable to deal with his complexes (and at the same time is no longer able to repress them), and they've exploded out of him in a volcanic eruption of murderous hatred and evil.