What would be the disadvantages of using microwave irradiation for synthetic reactions?
Microwave ovens work by stimulating an absorbtion band in water molecules, heating them up. If the reaction you want is in water solution and accelerated by heat, that may work OK. Otherwise, either the microwaves may not be absorbed efficiently, or they may stimulate the wrong thing. If you used microwaves of a different frequency tuned to your reactants, that might be interesting and useful. However, AFAIK microwave ovens use a magnetron whose frequency depends on the physical dimensions (you can’t tune them like a radio), and they operate in a special unlicensed radio band. So you’d have to get a tunable oven, and check out the licensing requirements.