The starter in my 91SE often continues to run after the engine is started. Not completely though. The starter motor continues to spin, but it's not engaged. It's really dragging the battery/alternator down (the voltage often reads just under 14 when I'm driving), and I'm ofter needing a jump after I've reached my destination. I'm not sure if it's the ignition switch or maybe the inhibitor relay.
Either that or I'm completely delusional. I'm pretty sure it's the starter I hear running, and I'm not really sure why else my voltage would be running so low. If the alternator was failing I would think I would have bigger problems.