The Taurus, 96 and newer, does not really have the problems you're likely worrying about.
Head gasket problems were widespread on the 3.8L engine discontinued after the 1995 model year. You don't have that problem with an 01 or 02.
Transmission problems were mostly licked around the same time.
For best luck, try to avoid a plastic intake manifold (some later designs were fixed for this problem - but earlier ones had a nice aluminum manifold that was trouble-free). Also look for an AX4N transmission - the AX4S isn't bad, but the AX4N is definitely superior.
The 12V vulcan is known to be a relatively bullet-proof engine, but it does have its quirks. Its DPFE sensor is prone to failure, but is not very expensive ($40-50) and trivial to replace for a DIYer. The camshaft position sensor also causes some problems and is a bit more expensive to replace ($300-400 at a dealer). They tend to last 80-120k, though, so constant replacement is not an issue. The 24V has the same DPFE sensor issue, but the camshaft position sensor is not a problem. They tend not to be quite as reliable overall, though (it isn't a tank of an engine like the 12V)