Last night after hours and hours of gameplay I found a very frustrating bug. I was completing the first Brotherhood of Steel mission and found myself needing to exit the mission area via an elevator. I would enter the elevator and in a few minutes find that my companions and I were in the elevator, but the elevator door would never open. It seemed my game was stuck. I tried going back to an earlier game (several times) but no luck.
I was about to give up, but I gave it one more try and it paid off. Instead of just loading a prior save, I actually returned to the Xbox hub and close out Fallout 4 (using the 'start' menu and selecting "Quit Game"). Then I reloaded Fallout 4 and launched from my last save point prior to entering the elevator. Also, I changed from 1st to 3rd person mode when entering the elevator. One of these two things, either closing and restarting the game or changing to 3rd person, flipped something in the game and I was able to continue my progress. Knowing what I do about software engineering, I'd say it's more likely the former but as buggy as Bethesda games can be it could also be the latter.
So in short, if you find yourself unable to progress because you keep getting stuck on an elevator, don't panic. Save your game (before entering the elevator), close Fallout 4 completely from the Xbox Hub, reopen Fallout 4 from your last save and try again. If that doesn't work, try switching from 1st to 3rd person. Also it goes without saying that you need to be saving your game often. There's a Quicksave feature and I recommend using it often. And always save before entering an elevator!