Does a rear wheel work up front? Assuming that the wheel will fit in the drops, will a rear wheel (minus the freewheel/cassette) work for a front wheel?  What kind of problems could this present?

I happen to have a spare back wheel for my bike (without the freewheel on it) and wonder could I if my front gets totaled.
Most bikes use 100mm in the front and 130/135mm in the back, so its unlikely it would fit unless you knew a priori that your bike was one that could have it fit. 

However, some bikes are designed for running rear hubs in the front (Surly Moonlander/Pugsley, for example).

A non-Fat Bike case is the Salsa Enabler.