Commonest complication of Caldwell-Luc operation is
"The most common complication is paresthesia of the cheek, teeth and gingiva secondary to stretch injury of the infraorbital nerve". ─ Microendoscopic surgery
"The most common complication is postoperative hypoesthesia of cheek and teeth". — Head & Neck surgery : otolaryngology
Complications of Caldwell - Luc operation 

Postoperative bleeding. This can be controlled by a nasal pack
Anaesthesia of the cheek due to stretching of the infraorbital nerve. It may last for a few weeks or months.
Anaesthesia of teeth
Injury to nasolacrimal duct
Sublabial fistula (oroantral fistula)
Osteomyelitis of maxilla (rare)
Oroantral fistula
Infra orbital nerve palsy
Haemorrhage
Orbital cellulitis