One of the ways you can check for other leaks is to fix these first. Then, fill the water tank and turn on the pump. Open all the faucets and run enough water that you bleed all the air out of the system. This may take a while because you'll have a lot of air trapped in the hot water heater. After all the faucets are running smoothly, shut them off and leave the pump on. If the pump occasionally turns on, it likely indicates that you have a leak somewhere in the system that you need to track down. If it stays off, you're most likely good!