If the CEL is solid get it ran at autozone so we have more information to work with. Did you notice if your idle was getting too low? That can be caused by a few things, one mentioned by the previous poster. 1-the idle mechanisms need to be adjusted or thorougly cleaned. Have you cleaned your throttle body in the past few years? It's a good idea to clean it when you change your air filter.
2-bad ground or battery dying. The rationale behind this is that your car is generating enough power while the motor is spinning at higher RPMS [not at idle] because of the alternator but once you stop moving the battery doesn't contribute and causes the car to struggle to hold idle. This can also be a sign of a failing alternator, again you can check this for free at autozone.
3-maint. items. If your plugs/cables are original they can become loose and you may not notice it while driving but while idling it'll become much more evident.
You can try checking here for more info on each of those and work your way through it. Here is a good place to start
mustang shakes. You want to fix it before you can't maintain idle half way to work and end up paying 100+ for a tow and a shop getting 80 an hour that you could probably solve yourself.
problems with my v-6 
