Not sure about the hesitation but my manual 325i does the idle drop all the time when coming to a stop but I've given up trying to fix it.
I don't think it's an auto-specific thing and can be caused by all manner of problems, some of which have already been mentioned.
If you can be arsed, try disconnecting the MAF sensor and see if it goes away like it does with mine.
NB doing this will throw a code and you will lose cruise control and the ability to heel-toe, which is no biggie in an auto unless your wife likes to stall it up on the brake at the lights or is a habitual left foot braker.
My theory is that disconnecting the MAF sensor forces the DME to use a basic failsafe mode or map for airflow.
With this basic (ie rich) map, there is less tendency for the idle to hunt around trying to chase some sort of balance that might otherwise be affected by a leaky, dirty or faulty component elsewhere.
Of course I could be on drugs but I'd be interested to hear what you find if you try it.
This doesn't necessarily tell you where the fault lies either but in my case it wasn't the MAF sensor.......or the DISA, OSV, CPS, CAS, ICV, VANOS, TB, coils, plugs, boots, gaskets, battery, fuel filter etc.