Upstairs, Downstairs/WMG

Alfred is autistic
His speaking predominantly in scripture is a form of scripting (a behavior that's a common symptom of autism), plus a lot of the things he says sound like they could have come from Mr. Hudson or Pierce. Plus, problems sleeping can occur along with autism, and it could explain why he terrorizes Sarah in the first episode by quoting at her and grabbing her wrist, yet no-one else is bothered by his behaviors and simply says he's "a bit touched in the head", and by the time of "Board wages" she clearly sees no reason to be afraid of him, suggesting he didn't actually mean to do her any harm.

Mrs. Bridges is Ruby's biological mother
She got pregnant by a Gypsy and was going to run off with him, but for whatever reason (maybe she still lived with abusive parents at the time or something) she wasn't able to and was forced to give the child up for adoption. She probably barely even got to see the child, but maybe overheard a doctor say it had some condition that would affect its brain, and she may have even known the gender. Because of this experience she has strongly maternal feelings for simple Emily (who reminds her of her lost daughter) and for mentally unwell Alfred (who Rose mentions Mrs. Bridges looks after), but despite her best efforts her abusive childhood makes her wind up treating Emily horribly at times. She gets a wake-up call to what a jerkass she was to poor Emily, and when she was later reminded of her lost daughter again by Ruby (her actual child), she was able to treat her far better.

James Bellamy was the father of Katie's baby
Either Sarah wasn't the first maid he seduced, or she "entertained" a group of soldiers that he was amongst.

Emily has Fetal Alcohol Syndrome
And her mother either couldn't keep her children's names straight when she was drunk, or Emily and her siblings were actually raised by their grandmother (but thought that she was their mother) and her forgetting their names was actually her dementia setting in.