So the settings were as follows:
Halo 4, level Midnight on legendary, Co-op, 2 player local.
Iron skull was on.
Yesterday we tried to play through the broadsword section, but unable to succeed. Thus, we gave up for the day to try again today.
What happened, was: The game seemed to be on “pause” by the player 2 when we started the X1 again today. Unpaused-> the game continued from the beginning of the broadsword phase. BUT, the HUD was gone for the both of us, and no flight instructions were visible at the beginning as it should be for the first minute or so. Also, the menu button didn’t work for either of us. We ignored this for a while, until decided that this must be fixed, 'cause it’s harder to fly without shield indicator etc.
We rebooted the X1, but the problem stayed nevertheless. After that, we took the disc out of the console and put it back in. The problem stayed.
After that, we took the power cord off the wall and reconnected. This time, it worked, and we were able to reload the game from the menu and select the game and mission parameters as normally.
Also, I thought it was weird that we got no checkpoints during the broadsword run, as in X360 version there has been checkpoints during the flight. I know that we had the iron skull on, but in co-op the checkpoints came normally in previous maps and after finally completing the flight. (Attempt no. >9000)