I would imagine that it would have some effect over the long-term. Humans are wired to sleep at night and be awake during the day. Even though we can train ourselves to get used to a reverse schedule, I think that we are going against our evolutionary nature.
Just for starters, there is definitely evidence of a link between our exposure to sunlight and our happiness and mental well-being. Someone who sleeps all day significantly decreases their exposure to sunlight, and therefore may be increasing their risk of developing depression.
In addition, many people who work at night may develop a feeling that they're missing out on what's happening in the world around them. The vast majority of us operate during the day, which may cause a night-shift worker to begin feeling secluded and left-out. Over a long period of time, this may also have an effect on a person's mental state.