There isn't really very much that's Classical in Harry Pottter 7b - aside from the usual Latin names and spells - but I'm nothing if not a completist so I'm covering it anyway! Spoilers follow.
Harry Potter 7b (thanks to Kermode and Mayo for that nickname) does contain a dragon, so perhaps this is a good time to discuss ancient dragons. Dragons as we imagine them are generally either Eastern (the long ones, especially if they're friendly, like that one that looks like a dog in The Neverending Story) or Norse (the fire-breathing, treasure-hoarding ones). However, the word 'dragon' comes from the Greek drakōn, Latin draco, both of which essentially mean 'large serpent'. In Classical myth, a dragon is long and toothy, more like an Eastern dragon or perhaps a wyrm-type of dragon, but it doesn't really have any special qualities other than size. A dragon guarded the Golden Fleece, but that was more because it had been placed there as a suitably scary monster rather than because dragons had any particular connection with treasure hoarding. Whereas modern pop culture dragons, aside from usually having a heavier shape, tend to have certain qualities - cleverness, a weak spot in a thick hide, a fondness for treasure - ancient dragons really are just big snakes. The dragon in the film is definitely a modern-by-way-of-Norse dragon.
The dragons that pull Medea's chariot as she makes her escape, and the dragon that guarded the Golden Fleece swallowing Jason - as you can see, they're basically just big snakes.
Draco Malfoy's first name, of course, means dragon, but it is also the name of a legendary ruler of Athens who brought in a set of incredibly harsh laws in which the death penalty was laid down for just about everything. These laws were repealed by Solon, except for the murder laws, and it's Draco of Athens that gives us the word 'draconian' for a particularly harsh set of rules. Draco Malfoy is named for the mythological creature - in fact, for the mythological creature in its Classical, big-snake form, given that he's a Slytherin through and through. But I can't help feeling that the most harsh of the ancient law-makers is a pretty suitable connection for him as well!
I really enjoyed the film, and almost everything I wanted to see in it was there. (The exception was the wonderful scene where Professor McGonagall enchants a bunch of school desks to go after the bad guys, which I loved, but I understand why it wasn't included). I was a bit sad to see Draco still refusing to stand up for, well, anything, but I'm very glad the scene with Narcissa and supposedly-dead Harry was kept, which was one of my favourite parts of the book. Mrs Weasley kicked bottom, though I expected her to shout louder! Poor old Fred's death scene got a bit curtailed, which was a shame, and I wanted Neville to kill the snake in front of the whole school, not just Ron and Hermione. And the entire film felt a bit like one big climax with no build-up - since all the build-up was in 7a - which I guess is justified after ten years and eight movies, but does make it feel a bit incomplete. Though we did get to spend almost all the movie in Hogwarts again, which was great.
There were some parts I absolutely loved. Neville and Luna make a great couple. Perhaps my favourite moment of all was Professor McGonagall telling Mrs Weasley that she'd always wanted to do the spell that makes the statues turn into an army. Helena Bonham Carter as Hermione on Polyjuice Potion was completely wonderful and, bizarrely, had better chemistry with Ron, though the kiss in the Chamber of Secrets was nice. Ron yelling 'that's my girlfriend!' like he's secretly been wanting to do for eight movies was good too. Snape's death and the revelation of his memories were great and I cried - I especially loved that they got the shorter wig back for some of the sequences set in the past - though I did wonder how Voldemort thought he could win the wand from Snape if he got a snake to kill him (because he disarmed him I suppose).
The epilogue worked better on the film than it did in the book for me. I think it's because the railway station is such a symbol of the world of Potter, because Harry's offspring is trundling along an identical cart to Harry's and most importantly, because the original John Williams score comes back. The use of the first movie's music all over the end section - with it's more magical, enchanting and especially more upbeat sound! - really brought the story full circle and was the perfect way to demonstrate that all is well in the wizarding world once again. It was like that moment at the end of Revenge of the Sith where the two suns appear on Tattooine and the original score plays and you just want to watch the whole set of movies all over again from the beginning (in Star Wars' case, from No. 4, of course). It's actually the perfect ending for the film and for the series, and I foresee many circular viewings of the films that both start and end with the flawed but magical first film in the future!