The best way for problem-free garage doors is maintenance. This might be old news but as fresh as it has ever been! Let's see it from a different angle! What do you do? Don't you go for annual check-up to avoid health problems? What makes you think that your overhead door doesn't need annual check-up, too? In fact, on many occasions and when the system is old or over-used, troubleshooting it more often will only have benefits to both you and the mechanism. The system will be stronger and more resistant and will last for ages. You will not have to deal with problems every now and then and you will feel more confident when you press this little button on the clicker.
There are tens of garage door parts and it's certainly best to avoid repairing them when there are real problems. Though, you can inspect them visually and pay attention to noises. More particularly, you should focus on main components, which will make a difference to the performance of the door or your safety if they fail to work properly. This way, you can prevent problems by fixing them as soon as possible.