I know this is a horror movie, and you shouldn't expect them to be logical in a way more realistic movies are, but it seems there are several things that don't make sense even according to the movie's inner logic. Here are some questions that are left unanswered in the film:
Why does the Mothman appear to Mary? Is it trying to warn her about her brain tumor? But all the other warnings the Mothman gives are about larger catastrophies where several people will die, so why was this one woman so important?
Why does Gordon think John has rang his doorbell for three nights in a row, even though John doesn't remember any of it? Was the Mothman posing as John? If so, why?
It seems the reason the Mothman is drawn to Point Pleasant is because it can sense the coming catastrophe at the bridge. But why does it also prophesy about other catastrophes in other parts of the world? Were the people involved in those other catastrophes also visited by Mothmen before they died, and did those other Mothmen also tell them about the upcoming accident at Ohio river?
We find out that the Mothman can speak with a human voice, so what was the point of all those telephone calls with the high-pitched electronic noise?
Why does Gordon freeze to death? What was he doing outside? Did the Mothman lead him there? If so, why? Previously the Mothman appeared to be friendly with Gordon, why would it want him dead?
Is the woman who Connie saw the real Mary, or the Mothman posing as Mary? If it's the latter, why did the Mothman do this?
Why does the Mothman first warn John about the Silver Bridge accident, then try to get him away from Point Pleasant by claiming Mary would call him? If we accept Connie's dream as a vision from the Mothman, then there was only ever going to be 37 victims in the accident, meaning that John wasn't going to die in it. Why, then, does the Mothman try to lure him away from Point Pleasant when the accident was about to happen?
The accident happens when cars are stuck at the bridge due to some odd malfunction in the traffic lights. It's also said the cause of the bridge's collapse is unknown. All this hints that the Mothman was actually behind the accident. But if it was, why was it also trying to warn people about it?
All of the above being left unexplained is the central theme of the movie. You can't understand the creature's origins, motivations or even its basic nature, and if you pursue these questions, you're basically driving yourself to obsession and eventual insanity without anything to gain from it.
Imagine a creature further advanced than you are you are to a cockroach. Imagine trying to communicate with the cockroach. As stated, the entity was intrigued by people who noticed it, but its ability to communicate with us is fractured, at best.
There be no entity at all, of course. As Leek mentions, these visions and experiences might be the equivalent to hair being raised just before a lightning strike.