Is there an improper way to connect water lines to water heater?
There is a way that cold water would mix prematurely with the hot water.  This could happen if there is something wrong with the cold water dip tube.  The cold water dip tube takes the cold water from the connection at the top of the tank to the bottom of the tank where it is heated.    If the dip tube becomes faulty or is removed, the hot water from the tap will run out quickly.  

Failure of dip tubes is common, especially with water heaters from the mid 90's.  There is also the outside unlikely chance that it was removed when replacing the pipes.

Of course, you get the same effect if the hot and cold connections are reversed.