Into the Woods/WMG

Cinderella's Prince is a Time Lord.
Hear me out.

The Wolf and Cinderella's Prince are often played by the same actor. This is because they are in fact the same person. We meet The Wolf, who is killed before we meet the Cinderella's Prince. They are both very womanizing and, most importantly, have repeated lyrics. "...so many worth exploring | Just one would be so boring." How else would they both have known those words? Everyone thought the Wolf had been killed, but instead he regenerated when no one was looking. He then returned to the castle and attend the festival. Due to a freak accident his mouth is the door to his TARDIS, which is how he fit two whole people, totally alive, in his belly.

The Witch didn't die.
She simply placed the curse upon herself again, her beauty gone but her powers restored. All that smoke? The curse taking effect. She then promptly magicked herself away. "Give me claws and a hunch, just get me away from this bunch."
 * Most versions, though, give her a lengthy scream as she disappears, implying her fate is far from pleasant.
 * Having your body aged and twisted could well be incredibly painful.

The Witch and the Baker's Father had a fling.
It was brief and lasted while the Baker's Mother was pregnant; the Baker's Father had fallen out of love with his wife and liked the Witch's exoticness. The Witch went along with it for a lark until the beans were stolen. Besides, just listen to the dialogue between the Witch and  - don't they sound like a pair of warring exes? Also, it's nice irony against the Baker, whose Wife (briefly) fell out of love with him.
 * Gives a new meaning to the line "He was robbing me! Raping me!", that's for sure...
 * Then why did he steal the beans in the first place, if not for his wife's yearning? Of course, one response could be the Baker's Mother was going to leave with the Baker unless the father proved he loved her by taking the beans. He decided to break off the fling and take the beans after one final time.

Jack's dad isn't dead.
He left his family when Jack was very small to seek his fortune, and is now the hero of another fairytale somewhere far away-- probably, given the world they live in, a fairytale that involves realising how callous it was to leave his wife and child for twenty years without sending back word, and discovering that he can't find his way back.

Somehow, this (or a vaguer version of it, anyhow) is how Jack's Mother's line "Your mother's getting older, your father's not back" always read to me as a kid-- at least in the American Playhouse taped version, her delivery sounds more like resignation to the fact that he's not returning than that he's dead but she doesn't want to tell Jack.