Here are the steps I took:
1) Played most of the way through Episode 1, only ever using Slot 1 (always HDD, never Cloud).
2) Started a second game in the untouched Slot 2, didn't go far; no issues up to that point.
3) Finished Episode 1 in Slot 1.
4) Used the "Copy" feature to backup my main game from Slot 1 to the also-untouched Slot 3.
5) Based on the excellent(!) experience up to that point, got optimistic and installed Episodes 2, 3, and 4 at once.
6) Went back into Slot 1, and played part of the way into Episode 2.
7) Wanted to go further in my Slot 2 / Alternate choices game, but instead of recognizing that I should have still been in Episode 1 there, it auto-shifted over to Episode 2, even though I'd never completed Episode 1 in that slot, nor copied a game there. When I attempted to nudge it back to Episode 1 with LB and resume playing, it gave me a "you will lose progress past this point" warning.
8) I got freaked out and started reading the internet.
9) I tried the "start game, sign out of gamertag, go back into game" suggestion, no dice.
10) At this point there appears to be only *one* saved narrative-- whatever has been saved last in *any* slot-- even though Slots 1-3 still show the correct timestamps from when I last actually saved to them.
NOTE: I have *never* played Episode 3 or Episode 4 at all, and have never completed Episode 2.
Please fix, or at least tell us where we stand!
p.s. If it might matter, I have a Xbox 360 250GB (black, bought new summer 2011).