Rough. This almost happened to me flying UA out of SFO. The app wasn't even wrong -- I just screwed up the gate number in my head.

Luckily the flight leaving from the gate I was at was leaving before my flight so I didn't miss anything. I got in line at the gate and thought, gee, they are boarding early! Then I heard something about chicago, looked at the monitor, said, hey, I'm going to Hawaii... and had to duck under the little barrier like an idiot to get out of the line.

Total dumb luck on my part -- had I been at the gate for a later flight I very well may have missed mine.