Why does Skyrim crash during the second half of the Waking Nightmare quest?

I encountered this bug recently as well, and in fact you do not need to complete the quest without saving (and good thing too, I was pretty underlevelled for it).

All you need to do is make your way outside and save there. This seems to clear out whatever it is that was causing the game to crash, and allows you to complete the quest with quicksaves:

1. Immediately after the Dreamstride, pull the soul gem that's powering the barrier out of the sconce its in. This takes down the barrier to the previous part of the temple.
2. The NPC Priest of Mara comes through the now clear corridor and blathers at you for a little bit about how amazing you are.
3. Run past him, up the stairs and out of the temple to Skyrim proper.
4. Save your game while standing outside of the temple - can be a quicksave or a full save, doesn't matter.
5. Go back inside the temple and complete the quest. You will be able to save.

Update: This issue has been fixed by the v1.9 patch.

Fixed a rare crash when attempting to save your game during "Waking Nightmare"

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From the UESP wiki's "Waking Nightmare - Bugs" article:

As of patch 1.8, saving during or after the Dreamstride portion of the quest will cause the game to freeze on consoles or crash to desktop on PC.

• To prevent this, avoid saving during this quest, and disable autosaves as well.
• (PC) (Xbox 360) Alternatively, after removing the barrier to speak with Erandur, simply leave the dungeon to go outside (in icy Skyrim), save outside, re-enter, and you should be able to save again normally.
• (PC) As the bug originates during the Dreamstride, use the console command tcl, cross through the barrier, and remove the soul gem. Since the quest progress is scripted through the status of the soul gem, this will progress the quest just as if you had used the Dreamstride. The only impact it will cause on the game is that there will be no enemies except two orcs in the dining room, Torek and Veren.
• (PS3) The least complicated method to avoid this bug is to exit to the outdoor before and after the dreamstride. Exiting before the dreamstride will enable you to do it again after the dream, or else you will not be able to exit the temple at all.
• (Xbox 360) Using Ethereal shout may allow player to cross barrier, similar to PC console commands, with the same results. Saves work normally after this.