Gas range defective out of the box, what are my rights?

If the service person can fix the problems that the person who looked at it first seen and the stove works like it is suppose to, the dealer most likely will not take the stove back and most likely wouldn't be required to do so. I can certainly understand your position and concerns. However, you cannot go by "What might happen" as grounds to return the stove to the dealer. If it can be repaired and works as it is designed to work, I suspect you will have to keep it unless you get another one and discard this one. The repair person that comes out to repair the stove should make all the necessary repairs and check all connections for leaks before they ask you to sign any paperwork. If it were me, I would be there watching what is being done and making sure everything that is to be repaired gets repaired and all connections checked for any gas leaks. I would refuse to sign any paperwork if this wasn't done to my satisfaction. If once the repairs are made and you still have problems with the stove, you would need to call for the service tec to come out again and see if it can be repaired and if they give you a hard time about it you could contact the BBB and advise them of the situation or go to small claims court and try and get the problem resolved in front of a judge. Business do not like for the BBB to be calling them because it gives them a bad name and people checking up on a company will see and read what has happened. Your situation is kinda like buying a new vehicle. You buy a new vehicle and the next day the air doesn't work, or the windows will not operate correctly and keeps blowing fuses. The dealership where you bought the vehicle will not give you another new vehicle. They will make the necessary repairs to the vehicle to make it work as designed to do. Same with your stove, they will attempt to make all the necessary repairs first before they would take the stove back and give you another one. Once they come out and say they have it repaired, make them go through everything with you and show you it works correctly. If it messes up again, get them back as soon as you can so the warranty covers any future problems.