Hair: I found it a bit odd that they chose to give modern Crowley basically the same hairstyle as the Tenth Doctor (Series 2-4, not the awful DotD style) - but then I thought about it and decided there wasn't much choice, really. As long as they wanted Crowley to have short hair, they could either comb down the front or make it sticky-uppy - though he does have gorgeous hair, DT doesn't have many options with it. Crowley just wouldn't be satisfied with tame hair, and so there you go.
When Crowley is first appears in the show, it's eleven years ago in the graveyard, and he's got long flowing locks. However, in the script he's described as having a hairstyle that's stylish and fashionable for the late oughts - which is exactly the time when DT was playing the Tenth Doctor and being celebrated for his "really great hair". It seems that through the process of costuming and character design, the oughts hairstyle came out to be more fitting for the late teens. Funny how that came full circle.
Magic: One of the cutest scenes was when Aziraphale decided to do his magic show at Warlock's eleventh birthday party and Crowley tried his best to dissuade him. ("You can do real magic! Why do this?" "Because it's fun!" "Fun? It's humiliating!") Everyone can relate to Crowley's mortification at Aziraphale's complete lack of self-awareness, and you know he just wants to sink into the floor as he watches his best friend's horrible performance.
It reminded me of Destruction and Barnabas from Sandman. In case you're not aware of the characters or the story, Destruction is one of the Endless and is the embodiment of the concept of destruction, but he abandoned his duties and left. He spends his immortal life wandering and, at odds with his nature, attempts to create art, music, and poetry. He's terrible at it by nature (he's the embodiment of destruction and cannot create), but has no idea (and no idea why). We are treated to a story about him and his intelligent, talking dog Barnabas living on an island off Greece, where he paints pictures and composes poems and subjects Barnabas, his only audience, to them. "I've just completed my poem. Ready to hear it?" "As ready as I'll ever be." There's also, "I thought dogs were colorblind." "Looking at that painting, I thought you were."
It's obvious that after years of being with Destruction, Barnabas has abandoned trying to tell him that he's terrible at art and has taken to creative insults. However, the feel is the same: a loyal companion taking on the shame that the performer is unaware of. Barnabas wouldn't care if he didn't love Destruction, and the same goes for Crowley.
History: Neil Gaiman wrote the historical snippets for the first half of the third episode because he realized that there was a long stretch of story at that point that didn't involve Aziraphale and Crowley and he wanted to give DT and MS something to do. He used it to tell the story of the friendship between the angel and the demon, which wasn't explicitly described in the book, and it's one of the best sequences in the series.
He also used it to explain a few small details to add consistency to the world. An obvious example is showing how Crowley came to know Shadwell and started funding the Witchfinder Army. While it's not necessary to know how it happened, it's nice to get that background. After all, Shadwell is the only modern character in the book that has a prior association with the angel and the demon, though he had no idea who they actually were.
The short encounter with Crowley also filled out Shadwell as a character. In the book and up to this point in the show, Shadwell seems to be just a misguided madman, obsessed with imaginary witches and making up an army to con Aziraphale and Crowley out of their money. However, we learn that he truly believes, that he is convinced he and the army are the only things standing in the way of Hell, and that what he is now is a product of decades of fighting the good fight in a world that mocks him for his devotion.
There are two other tiny details that the historical scenes provide that add to the cohesiveness of the overall story. First, Shadwell joins the 60s caper because Crowley needs a lockpicker and Shadwell has the skills, explaining how he's able to pick the lock to get into Aziraphale's bookshop two episodes later. Second, when Satan is approaching, Aziraphale begs Crowley to do something, and he stops time to give them the opportunity to prepare Adam for his final task. Crowley has the ability to stop time? Of course he does: we saw him do that during the Reign of Terror in Aziraphale's cell. The angels and demons (and possibly individual angels and demons) have discrete sets of powers. Both Aziraphale and Crowley can, for example, heal bikes and cars, but Aziraphale can sense love while Crowley can sense evil and psychically detect observers. In the book, the final scene does not include a time stop - they have a different talk with Adam during the half-minute before Satan arrives - so the show not only introduced a different power for this scene, but seeded it early so that it wasn't a McGuffin.
Aside: Interestingly, in the book, Crowley is the one who resurrects the dove, not Aziraphale.
Second aside: Angels and demons apparently can sober up by undrinking their alcohol. Isn't it amazing how little alcohol they consumed over six hours of drinking solidly (two inches of a wine bottle?) and how drunk they got off it?
Okay, that's enough stream-of-consciousness for now. :)