What are the most common irrigation system problems contractors run into?

Age and sun related deterioration.

Shallow lines in a sandy bottom

The most common problems in northern Indiana, i have came across is failure in weatherization.  I usually find several broken lines in systems due to freeze breakage.  The other problem mostly consists of Zone actuator failures. Some of the systems I come across were poorly thought out or installed. At that point there's very little you can do other than to replace the system in its entirety. Weather is usually the biggest factor in failures here.

Really common are electrical issues. Hunter actually plans ahead for a 4% electrical failure (within their warranty period) of some sort on their electronics in central Texas due to our dirty power grid. So lots of module failures, decoder failures, solenoid failures etc. 

I have run into a lot of homes where the homeowners installed it or a plumber installed it. valves where 1' above ground everything run in half inch. had to gut a few systems to get them running right. i would say more common for me though is people putting drip and spray on the same zone or spray and rotors on the same zone causing massive water inconsistency.