When thickening sauces, due to time constraints, my roommate almost always ends up making a cornstarch slurry and dumping that into the sauce instead of letting it reduce naturally. When would that be a bad idea? Or is it always appropriate to substitute?
Reducing a mixture is simply boiling out water present in the solution. Adding a starch (either cornstarch or other flours) doesn't remove that water but instead causes the starch to expand and "trap" some of the water.
Cornstarch in particular doesn't work especially well when there isn't enough moisture in the base mixture, or if there's too much fat or sugar present, so it's not suitable for really rich sauces, for example pepper cream sauce. It also doesn't work well in acidic mixtures like tomato sauce.
The worst thing you can do for a cornstarch-thickened mixture is to cook it at a high temperature (i.e. more than a moderate simmer) or for an extended period of time. These will expand the starch granules so much that they pop, breaking the cornstarch and causing the sauce to thin again. So, be very careful of cooking temperature when using a cornstarch slurry.
I have also found that cornstarch doesn't respond very well to cooling and re-heating, so it's not the best solution if you plan on saving some of the sauce for later use.