Once you determine the correct diameter, there will be only two potential significant issues in changing stems.

The first is the dreaded "stuck" stem where electrolysis has occurred between the stem shaft/quill and the inside wall of the steerer tube. For tips on fixing this, check out Jobst Brandt's article on stuck stems, or google "stuck handlebar stem."

The second issue is less obvious, but potentially dangerous. Don't raise the stem above the minimum insertion line engraved on the stem. If the line is visible above the headset lock nut, it's too high and could accidentally come out while riding. If the stem doesn't have a minimum insertion line, a good rule of thumb is to have at least 2" of the stem in the fork steerer tube.

Just as having the stem too high, it can also be too low. Most steerer tubes are internally butted at the bottom where the tube is brazed to the fork crown, and if the quill is too low in the steerer it can be in the transition area between the non-butted and butted sections of the tube. You may think it's secure, but when riding the stem quill can lose its grip on the wall of the steerer, come loose, and ruin your day.

Both of these potentially dangerous conditions are explained in Sheldon Brown's article on adjusting handlebar height (scroll to the bottom of the page for a good illustration by Nicholas Flower of the problem encountered when the quill is in the transition part of the steerer tube).