Sometimes I close off 3 heat vents in my home.There are cold air returns in all rooms except a very small bathroom
The key words in you question are too many. How many other rooms do you have? more than 3? then you are probably OK. But be smart too. The cold air returns (unless you cover them up) will continue to draw cold air from the returns but not as great of a rate because of reduced pressure and then draw air from under the door if needed (unless you seal that too - please don't). This will increase the pressure in the rest of your system/house. For the most part this is not a big deal unless the three rooms represent a majority of your home. Heating systems are designed on cubic feet. if you reduce the amount of cubic feet then you reduce the amount of heat required. I believe you are trying to save fuel cost. Just make sure the rooms don't get too cold. Sometime just closing the vent MOST but not all of the way is the wiser decision. Stay warm!
If you block off too many registers you will restrict the air that moves across the heat exchanger. This could cause it to cycle off and on with the limit switch and ovber time could crack the heat exchanger due to extremes in temperature.
There should be no problem with that. If heat does not reach the thermostat you may have more hot air blowing out of the open ones. If your returns are open and clear you are all set. When you close a feed it only forces more air to open vents.
