What are the problems associated with the Y-Y three phase transformer connection?

Your third leg is called the high leg and can exceed 180 or more volts. In a 3 phase panel you will loose a third of your circuits unless they are used for motors or other equipment that uses three phase evenly through its function {meaning it doesn't use one leg exclusively for controls or 110V functions. It get a bit involved explaining the windings of a transformer and center taps but suffice it to say one leg gets more than it's share of windings in the transformer. It was used in the early years of industry when single phase 240V systems were the only game in town and they wanted to get more power from the Wye set up prior to delta. It never was popular but a necessity for industry and grew only because of slow development incorporating the 208V delta 3 phase system.