Commonest complication of Caldwell-Luc operation is
Oroantral fistula
Infra orbital nerve palsy
Haemorrhage
Orbital cellulitis
"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)