It really depends on what you're making and if it's possible to automate testing AND if you remembered to test it. Chrome appeared to have broken full screen movie playback for 5% of users once. Something changed, perf got bad, people who previously could play full screen video on a low end machine suddenly got playback too slow to be useful. They just stopped going full screen. No bug reports came in. Nothing in the testing infrastructure caught it. I only notice because my father tried to show me a video on his atom based netbook.
Similarly going full screen on a 2 monitor setup broke once. Again, no automated test.
The Web Text to Speech API is broken on every browser it's in. It will work with a simple sample but start and stop it a few times and it will break. I suspect because again there is no easy way to test it.
There's lots of others.
automated testing is not a substitute for QA IMO.