What would be the effect on Earth if the Moon’s orbit somehow shifted so that it was closer to Earth?
Likely very bad. Particular considering the Moon wouldn’t just shift orbit on its own.
Let’s just pretend it tip-toed over.
My guess would be that the Earth would slow down it’s rotation. And also would have an effect on the ocean.
Mainly the tidal fluctuation of the oceans would be more prounounced, the high tides higher and the low tides lower. The timing would be different too, although we can’t say how without more specific information on the change in th emoon’s orbit.
Also, the acceleration in the orbit of the moon would mean that the moon’s “day/night” cycle would no longer be synchronized with its orbit around the earth. So we would no longer have a “dark side of the moon” that couldn’t be seen from Earth. In a 28-day period, we would see the entire surface of the moon (I think).
We’ be drowning in werewolves!
It would have an effect on some plants and animals, due to a slightly brighter average nighttime.
If the distance decreased, the orbital period would also decrease; tides would be more frequent; changes of moon phase would be quicker.
The Earth’s rotation would also be slowed due to the increased friction. It’s slowing anyway, but this would increase the deceleration.
Also the danger that this alteration, if not accompanied with an increase in velocity, would put the moon into a spiral, with it continuing to close on Earth. This is what’s happening to Mars’ moon Phobos.
What if? What if? What if?
It would take a cataclysm of some sort which would be disruptive of the orbit of the earth as well as the moon.
Probably the most superficial change is that you’d no longer see the sun’s corona during a total eclipse. Likewise, a greater area of the earth would get to see the totality of said eclipses.
Zev Steinhardt
Just putting my slightly off topic two cents in. The moon used to be a lot closer (like, half the distance) to the earth in the olden days. OK, the way olden days, billions of years ago.
It has been moving away from the earth ever since. I think they’ve pegged it at about 1 cm per year. They can tell because of some laser reflectors left by the Apollo astronauts. Yup, they fire powerful laser beams at the moon and time the return (they make sure no aircraft are flying overhead before they shoot).
And, yes, what the others have said is correct - if it somehow moved in closer: tidal effects would be greater; solar eclipses would last longer (and there would be fewer annular eclipses (where the moon doesn’t cover the entire disc of the sun because it’s too far away); the moon would be brighter and drown out even more dim stars; and, of course, since the amount of time to orbit the earth would shorten, menstrual periods would be shorter, too. 
If the Moon were brought slightly closer, it would just look larger, brighter, and take less time to go through a cycle of phases. The difference it makes on the Earth’s rotation would probably not be noticeable in our lifetimes.
If it were brought much closer, to about 26,000 miles (semi-major axis) then it would be locked with the Earth’s rotation and would hang in roughly the same part of the sky all the time. Consequently it would only be visible from one hemisphere. And, it would stop receding. Of course, you’d have to scoot a lot of geosynchronous satellites out of the way first.
If it were brought closer yet, it would rise in the west and set in the east, and would start to get pulled inward so that after enough time its orbit would decay completely.
If it were brought too close, within the Roche limit, then the Earth’s tidal forces would tear the Moon apart and our planet would have a ring. Wikipedia gives a distance of between 9 million and 18 million meters, or about 6,000 - 12,000 miles.
Rather than having the Moon move closer (or farther away), what would occur if Earth had two moons?
I’m pretty sure you’re joking, but are menstrual cycles really dependant on the lunar cycle or is it just a coincidence?
I’m totally joking! :wally
(You know, even though the “putz” smiley is offered, and I just used it, isn’t it too harsh? I mean, I think it’s funny to call you a putz, but I don’t even know you.) 
It is just a coincidence. But the word menstrual is derived from moon because of the similarity in the length of time. That’s why I made the joke.
I’m suprised no one has mentioned the weather yet. Isn’t our mild weather system dependent on the moon?
We do get more rain around the full moon, if that’s what you mean.
Is that true?
I can’t quite figure out what the mechanism would be, and I would greatly appreciate a cite. (As no doubt would many other of our members.)
Trying to remember where I saw that. It may have been in Cosmic Adventure by Bob Berman, but anything in that book is like a needle in a haystack. Or, it may have been in his column in Discover magazine a while back. One might expect to be able to find many sites confirming or disputing this statement, but an extensive search turned up nothing.
As for mechanism, it is conceivable that spring tides -> more evaporation -> more clouds -> more rain? [/speculation]
No. Isn’t the gravitational pull from the moon responsible for the trade winds or something like that? I heard the reason Jupiter has bands in its atmosphere and storms that rage on for centuries is that the relative gravitational pull of its moons are less significant than ours. Of course the planet is a whole bunch bigger. But still, had we no moon I heard that our weather would be much more severe. In fact, it was said that the moon was one thing that made life on Earth possible, or at least liveable.