If you are thinking of using a mountain bike crankset on a road bike there are several possible problems although this has been down my many.

First of all, in many cases the front derailleur cannot be lowered enough to work acceptably with the mountain crankset. This is a common problem with braze-on style front derailleurs used as standard equipment on many modern frames, especially carbon fiber frames. This can also be a problem for a road crankset with small chainrings.

Many mountain type front derailleurs are top-pull which do not work with STI road bike shifters.

The front shifter cable pulls and actuation ratios are different from road bikes to mountain bikes.
As others have said, most rear mountain bike derailleurs are completely compatible with road shifters, including certain lower level 10-speed mountain bike RD's. Dyna-Sys rear mountain derailleurs have a different actuation ratio and are not compatible with road shifters.

Some 9-speed triple ring cranksets do not work well with a 10-speed chain if the ring to ring spacing is too wide. This falls into the "try it and see" category.