The main nerve of concern in dissection of the masseter muscle is the facial nerve - that is the one that supplies motor nerves to the muscles of facial expression (the ones that let you smile, frown, etc). IIRC, in order to access the area, most surgeons will make an incision around the ear and work the flap forward (degloving the area so to speak). Don't quote me on this btw, it's been years since I read up on it.
In doing so there is a risk of disturbing the parotid salivary gland, and facial nerve is in proximity to the parotid salivary gland.
Bruising of the nerve may cause temporary or even permanent paralysis of that side of the face (Bell's palsy).
Radiation therapy is generally avoided for the reasons someone previously mentioned - the collateral damage from radiation generally outweighs the benefits unless you're looking at managing a malignant tumour.