What are the possible complications and side effects of a brow lift?

That depends upon the type performed. Endoscopic browlifts generally have a very low risk of complications, but with all these procedures there is a risk of some localized hair loss, elevation of the hairline, scarring within the hairline, and numbness behind the incision (highly unlikely with the endoscopic approach).

There are many potential complications that can occur from browlift surgery. The technique with which the surgery is performed and the extent and location of the incisions will have something to do with the frequency of the complications. Your surgeons familiarity with the anatomy will also impact which complications can occur.
The list of any surgical complication will be included in your pre-operative discussion with your surgeon. However, the biggest potential complications that I would pay most attention to are injury to the facial nerve resulting in forehead muscle weakness and injury to the sensory nerves of the forehead resulting in forehead and scalp numbness. Other than these potential complications most of the other issues are generally temporary, of little impact to the ultimate surgical result and can be generally be corrected.

There are many methods for perfoming a browlift or forehead lift including an endoscopic browlift (through tiny incisions with the assistance of telescopes) , bicoronal forehead lift (extensive incision from ear to ear across the top of the head) and a tricophytic or hairline browlift. (hidden along the hairline. Each of these techniques achieves a similar result through the brow and the forehead in terms of smoothing of lines and gentle elevation of the brows.
The key difference is in how they affect your hariline. The Bicoronal (ear to ear) browlift elevates or pulls your hairline back, raising the frontal hairline by up to one inch. The Endoscopic lift has minimal effect of the position of the hairline. The tricophytic or hairline browlift can be used to adjust the hairline, usually lowering it to address a receding hairline or widow's peaks in the temporal hairline.