If that Mustang has a lot of miles and the oxygen sensors were never changed then change them. When you buy a used car expect to change a lot of things if not just one single thing. Old sensors working along with other older sensors through the car wreak havoc on the car's operation.

Clean or replace the idle air control sensor, make sure TPS is withing the .80 to .95 range, replace oxygen sensors, replace the coolant temperature sensor which sends the signal to the EEC (located on coolant return tube on right side of lower intake), get some CRC electrical contact cleaner and clean the "salt & pepper" connectors that are attached to the back of the upper intake running to the injectors (remember to use fresh electrical contact lube when reconnecting), and if the car has it's original TFI module these things can make the car run like a cinder block when they become hot/overheated. The MAP sensor is not that close to the brake booster. It's the black popsicle-shaped thing bolted almost center of the firewall above the upper intake and has a hose connected to it. When those get old they make the car run crumby, too. Gotta remember all these work in conjunction with one another and having a mixed bunch of old with new sensor is going to make the car run eractically.