More specifically:

Jupiter weighs almost 25,000 times more than the moon. Massive water tides kilometers high would wipe out large numbers of people initially.

Then, tidal flexing of the earth's crust (100s of meters a day)would cause a massive increase in *volcanism, probably wiping out many of those who are left. The crust will become very hot, exacerbating the next issue.

Those who somehow survived the above would find themselves on a world that was growing increasingly hot. Jupiter actually puts out a large amount of thermal radiation, as it is still slowly contracting from the days of its formation. Right now it puts out twice as much energy as it receives from the sun. Moved to earth's orbit, there's still going to be a large new source of heating that will drive earth out of its current equilibrium. **

Finally, earth's rotation will slow down, the energy having gone into heating the earth's crust and moving its orbit out. The earth would spiral away from Jupiter for the same reasons that the moon is spiraling away from the earth today, only at a much faster pace. Eventually, the earth will be tidally locked to Jupiter, and the tides and volcanism will subside, perhaps to the level of Io now.

Edit: there will not be increase sightings of people from Vulcan. :|

Edit again: I decided to add in another calculation that I did in another post that shows that reflected sunlight would also be a severe problem.

Scroll down to Internal Heat in this article: http://en.wikipedia.org/wiki/Atmosphere_of_Jupiter

We can extrapolate a bit further from the article:

Jupiter emits about 1 billionth the power of the sun or about 335 petaWatts.

Since it would be 400 times closer, it would add about .6% more energy to the earth's surface, not including what we would get from increased sun-light reflected off of the clouds.

I'm a bit tired to calculate the extra reflected sunlight that we would get, and it's not a trivial amount, but I'll try anyway. The moon has albedo of about .08, similar to coal. Jupiter has an albedo of .52, seven times higher.

The circular area of Jupiter for reflected light characteristics is 16060607043km2. The same number for the moon is 9478715km2. This is simply to calculate relatively how big in the sky they would appear. This means that a "Full Jupiter" would reflect about 1694 times as much sunlight if the albedo was the same, but it's not. It's seven times higher. Therefore, a full Jupiter would reflect 11860 times more light to earth than a full moon.

Since a full moon probably heats the earth by about .03°F according to a recent study, then we can extrapolate that Jupiter would add additional heating from reflected sunlight of about 335°F.

Sooooooo....when I set out to do this calculation, I though that the internal heat from Jupiter would be a big problem. Turns out that reflected sunlight would kill us all even without all the other crap.

To add injury to fatal injury, one likely effect of moving Jupiter to earth's orbit is that the upper atmosphere will heat up and expand a bit, making the effect even larger than I just calculated.