These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
YMMV: Call the Midwife
Artistic License - Medicine: Leaving her patient in 2x02 should have got Cynthia into a lot of trouble, and she was very lucky that no tragedy occurred between her leaving and her backup arriving, which meant that the whole incident could be dealt with quietly by Sister Julienne. Even so, her panic attack was completely understandable.
Crack Pairing: Out of the bowels of Tumblr sprang the Dr Turner/Sister Julienne pairing. Definite crack, especially given that Dr Turner is so desperately in love with Sister Bernadette he can hardly see straight (it's very mutual) and has been since they first shared a scene, and yet some find it strangely enthralling. The "logic" seems to be, "She is like an older Sister Bernadette, and he's in love with Sister Bernadette. Also, Jenny Agutter is hot."
Creator Worship: Not only has Heidi Thomas won rave reviews from critics, she has been passionately embraced by the programme's fanbase, most especially on Tumblr, where she is considered to be just short of God. (And there are those who would dispute the "just short of" modifier.)
"O Come, O Come, Emanuel" from the 2012 Christmas special. The solo is sung by Laura Main (Sister Bernadette), a trained soprano, and by Sister Bernadette herself in-universe.
For "Children in Need" in 2013, Stephen McGann (Dr Turner) and Laura Main recorded a version of "When I Fall In Love (It Will Be Forever)". The BBC released it as a music video, and then the two performed it live. The reaction of the fandom was predictable, to say the least.
The romantic subplot between Sister Bernadette and Dr Turner is an example of a storyline becoming an Ensemble Darkhorse; the pair's romance got, on average, five minutes an episode beginning with their first shared scene in 1x06, but has become tremendously beloved, not least because every second of that screentime went toward building an utterly believable relationship.
Unexpectedly, Jane Sutton (Dorothy Atkinson), the Shrinking Violet medical orderly who joins Nonnatus after Chummy goes to Africa. When she didn't appear in the 2013 Christmas special, much of the fandom started saying, "Where's Jane? We want Jane back!"
Narm Charm: Call the Midwife definitely contains a few elements that could be considered a bit... Narm-y. There's that treacly voiceover for starters, not to mention the endless references to 'doing it for love'. Hallmark moments occur at least once an episode. Such a bucketload of sentimentality really ought to be off-putting and yet somehow it just... isn't. (And even if you're terribly cynical and think that it might be, CTM always has the ultimate trump card of loads and loads of brand new real life babies. Watch it and weep.)
Nightmare Fuel: Pretty much anything involving the workhouses that used to be in the East End. They're never seen, but the effects on those who lived and worked in them are clearly visible. "The workhouse howl" stands out as a Nightmare Fuel.
Also, any time deliveries go wrong.
Replacement Scrappy: Averted. Chummy's temporary replacement Jane is an interesting character in her own right. Invoked in-universe when Chummy comes back; Jane worries that she was only there to "fill a gap", but the other girls reassure her that she's a part of Nonnatus now.
Tear Jerker: You are going to cry while watching this. Probably more than once — an episode. That is all.
That said, between Nora Harding's entire storyline, Trixie's near-rape, and the fallout of Dr Turner giving in to his feelings with his I Kiss Your Hand, 2x05 stands out.
Values Dissonance: It is considered merely strange that the family in the first episode has 24 kids (with the 25th on the way), not to mention that the husband apparently married the wife and brought her to England when she was 14. Sister Julienne even says that she might even have been younger than that, and in Real Life Jennifer Worth reckoned that Conchita was eleven or twelve when she left Spain.
Everyone, including doctors, nurses, and pregnant women, smokes. It's even a bonding moment for Sister Bernadette and Dr Turner after a hard delivery!
The resolution to Mary's story: her daughter is taken from her without her consent and put up for adoption, given that Mary is only 15, homeless, and both uneducated and untrained. This is portrayed by the priest as being the best possible outcome to her situation, but it still triggers a Heroic BSOD in Mary.
When the Redmond baby was abducted, no one apparently thought it was unusual that the mother left the baby outside and alone in her pram on the sidewalk of a busy street, while she herself stayed inside to do the laundry.
In 1950s Britain it wasn't uncommon for people to leave their babies in prams outside their houses while they did something inside. It was wasn't necessarily something everyone did, but it was considered safe to do so by the people who did. It was taken as obvious that sleeping outdoors was good for children, and many houses had no yard or garden- it was also normal for children from poor areas to play in the street almost as soon as they could walk (there were very few cars and so many children played there it was assumed the older ones were watching.)