I'm completely unaware of a new water heater being a fix for corroded copper. I haven't seen everything yet, but I certainly don't believe what I hear. There may be an issue with improper dielectric separation between galvanized and copper pipes. Or, just as likely, a poor soldering job.
Green on pipes is often caused by a plumber's (or handyman's) gloves covered with flux. As they work with the pipes, the flux gets spread all over. A good plumber replaces his gloves when they get enough flux on them. Sometimes, leftover flux on the joints will oxidize the copper, but it usually poses no problems.
Sometimes, an abundance of corrosive flux inside the pipe can corrode right through the pipe. If the pipe is failing because of a dielectric problem, there are usually spots, and they can also be green.