Hot surface indicator light stays on
If it is really a false positive - i.e., the light is incorrectly showing something on, but all burners cycle on/off correctly, then I see no real concern.

If one of the burners is not working at all - i.e., you turn it on, the light goes on, but the burner does not actually warm up, then this is also not a significant problem as you just can't make use of that burner until you fix it.

However, if you have a situation where the light is on due to a burner turning on and not cycling but STAYING on then this is a real safety concern as you could forget and turn on that burner and forget about it for a little while and end up with your house burning down.

Simple enough to test. One burner at a time, put a pot of water on. Turn the burner on medium and watch it for a while. If it cycles normally, great. If a burner stays on -- gets red hot -- and never cycles off, then you have a serious problem that needs to be fixed. If I found this problem and it only affected one burner, I would remove the knob for that burner to prevent someone (including myself) from accidentally turning on that burner until it is repaired.