It might be frightening to hear, but it is common to fly on a plane with various broken things. A pilot once revealed that he experiences at least one failure on a plane every month. They're mostly small things the passengers don't need to stress about, like burnt-out lightbulbs. But the chances are that you've flown on a plane with a problem and had no idea about it. If it's not major, they just keep flying.
Of course, things can be broken or stop working on an airplane, but they will only continue to fly if it's safe. No need to make all the passengers aware of it and cause unnecessary stress.