Miata rough running

To check if engine timing is off, have your mechanic check the timing between the crankshaft and camshaft by pulling the cam sprocket plastic cover off, and checking camshaft index mark against the top dead center mark on the crankshaft. This check is NOT an ignition timing check.
Check the fuel pressure with the engine under load. The spark plug wires may not be on correctly. (They may LOOK ok).
Change the fuel filter.
If the spark plugs and wires are antiques, donate them to a museum, and put new ones on.
Check the MAF (or, MAP), idle air control valve, and the throttle position sensor. And, check the wiring, and connectors, to all of them.