Pyewhacket, you're right about the number of servants, which surely is about actor costs, though there is also an ongoing narrative about how cuts had to be made after the war. The number and kind of staff they have doesn't really seem to correspond to the work that has to be done, either: there is no sign of any laundry taking place and after Daisy's promotion they seem to dispense with the scullery maid altogether. Seems like the only washing up that ever gets done is the silver and fine glass, which would have been done by the butler.
There is also much less contact between senior outdoor staff (head gardener) and house staff than you'd expect. Much less contact between these servants and other servants- who are the junior female staff hoping to marry? And the family themselves seem to live an abnormally reclusive life for their day and age.
As for the chauffeur-daughter affair though, I think Fellowes is building on actual events. He comes from an aristocratic background and a lot of the plot lines in Downton are things he has heard from his parent. Here I think one does have to distinguish between "things that would have shocked a certain society" and "things that simply could not have happened in a certain society".
(as a professional historian I've come across this quite a lot- the handbooks tell you what is unthinkable in this particular class/time and then your object of research goes and says and does that very thing)
Fellowes makes it quite clear that it is shocking, that Sybil does rather want to shock her parents (at least at first), she is growing up during the suffragette movement but can't actually smash anything because that's not how she rolls. By the time she runs away with Branson, she has worked as a nurse, treating soldiers, seen all sorts- she is not the sheltered little thing she was.
The hygiene thing, I think, is also a bit of a red herring, given the number of masters who had no difficulty in forcing themselves on their servants and mistresses who tried to manipulate male servants into sex. The Jimmy/Lady Whotsit storyline is perfectly plausible.