If you ever go through The Break of Dawn again, this is how you get around that issue: take your follower with you as normal and fight the boss. After he's dead, don't loot anything in that room yet. Walk back to the entrance of the dungeon, go outside, and tell your follower to wait there. Run back in and loot all the bodies, then take the sword. After speaking with Meridia, go back to the entrance of the dungeon where you left your follower.
As for Containment, the problem seems to only occur after asking your follower to wait, say in the Hall of Attainment, or outside in the courtyard while you enter the Hall of the Elements. After the blackout, they're suddenly there in the Hall of the Elements with you (still in their "waiting" state). If this happens, you shouldn't have a problem if you just ask them to follow you again on your way out. This happened to me a couple of times, so I actually took to just keeping my follower with me. It hasn't seemed to be a problem; however, I'm on PC with the Unofficial Patches, so that might account for it. If you're really worried about it, after leaving Mzulft, but before returning to the College, take them back to their home base and dismiss them, then go back and get them before you hit the next dungeon.
Japhet's Folly. I'd definitely leave followers home for that one.
Nightcaller Temple actually isn't an issue for the follower themselves: they just wait for you at the door. However, there was an issue with crashing during the dungeon portion which some had speculated had something to do with having your follower waiting at the door. It's supposedly fixed by the latest patch, though.
Without spoiling anything, all I'll say is: I'd leave followers waiting outside Kagrenzel (it's not a huge dungeon). And don't try to sneak in from the rear exit--sometimes that causes issues with followers as well.
Also, Sightless Pit can be problematic. You have to drop down into the dungeon, which can cause issues with followers pathing. Once inside, because of the drop, you cannot exit the way you came and must finish the dungeon to get out. Save before you enter! It's a Falmer dungeon and they can be really tough, especially for low-level characters. If you've bitten off more than you can chew, you can always reload the save.