Are there any significant differences between two Apple products of the same name but different part numbers (particularly FC371LL/A and MC371LL/A)?
The refurbished one probably has a different part number because it is refurbished now new.

It won't have anything "wrong" with it, but it is refurbished. Check the specs and compare it to the current production model. Typically they will say "late 2010 model" or something of the sort to indicate if this is different (hardware wise) from the current one.