were you told to heat it very slowly? but I bet this was hard to do and the Mg ignited and gave off the smoke/vapor. Some of the MgO that is formed escapes in the form of fine powder, why the smoke was white. Ideally the oxidation is supposed to go slowly to reduce this loss that occurs from the ignition. It would be best to cover the crucible completely to prevent loss of the powder, but agrobert is right that you also need enough oxygen.
(the crucible is heated well above the boiling point of water, so there is no moisture in the crucible by the time the oxidation occurs)
the reaction of Mg + N2 to Mg3N2 is a major byproduct - did your product look yellowish/greenish? if so then alot of the MgO that you were supposed to make went up in smoke!