Everytime we flush the toilet in the finished basement, which is hardly ever, about 3 hours later the whole house has a sewer smell. What is going on and how do we fix it?

I noticed today that my bathtub shower faucet has some risidual leaking when I divert it to the shower head. There is a gap/hole in the bottom of the bathtub faucet that lets the water escape down the drain and I disassembled it and looked for any problems and looks like all is good except for some mineral deposits. Nothing is leaking behind the tile that I can tell...Basically when you pull up the spout to diver the water some leaks out of the hole on the bottom of the bathroom faucet but I also have a ring between tile and fauet so nothing reaches tile that I could tell. Is this normal? Should I replace faucet. It isn't hurting anything that I can tell. thanX!