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.