Does having laser eye surgery give any long term side effects?

Rarely. Laser eye surgery (lasik or prk) is generally safe long term; however as with all surgical procedures there can be long term problems. These include chronic dry eye, thinning of the cornea (ectasia), glare, to mention just of few of the more common ones.
Yes. The short answer is yes, but as there are many different types of lasers used in ophthalmology this is a difficult question. Any laser surgery is going to leave permanent effects. Most people referring to laser eye surgery are speaking of lasik. Overall lasik is a very safe procedure although symptoms such as dry eye, and halo's are common in the first few months after surgery.