Is there a problem if the toilet stinks, even after cleaning it - it is like the water stinks. It seems to involve only one of our toilets in our home. Could it mean a sewer problem?

Stinky like sewage oddor or more like mold and/or mildew? Add a pint of fresh bleach to your tank, allow to sit for 10 minutes and then repeat once more. If the moldy smeel is gone you are good to go. If you still smell sewage I'd start thinking about the wax ring under the toilet.