There's been a (denied) rumour that HBO is going to develop the 'Harry Potter' stories to a series for streaming services. No doubt many fans who grew up with the movie adaptations would call this sacrilege. The truth is that the original movie series is far from perfect. Any new adaptation should take the following into consideration.
Give It A Sense of StyleNot to sound mean, but the first two adaptations that came to life are very vanilla. They look like every other family movie ever made and does very little to put a unique stamp on this version. The Prisoner of Azkaban was the first film in the franchise to do something creative and artistic with the look of the wizard world, taking cues from German Expressionist cinema. It's the stand-out movie for this reason. It's not the most book-accurate adaptation, but it's the best movie. Having a style bible for the art design, and taking the chance to really push the boundaries, would go a long way to improving the experience. Go a bit extra with it.
Also settle on a consistent look for floo powder. That's annoying. And how Polyjuice Potion works.
Background MagicThis is mainly a gripe with the first two movies, but certainly applies to almost all of them. There's just not enough background magic happening scene to scene, especially in areas with denser wizard populations. The movies should have been packed with easter eggs of small, off-hand magic that wizards would use every day. When Harry first arrives at the Weasley house, there's two magic things happening and he stops to gawp at both of them giving us a cutaway shot for each. Dishes washing themselves and knitting needles working alone shouldn't be worth this sense of marvel from Harry after a year as a wizard. They should be as fascinating to Harry as a microwave.
On that note, it's doubly ridiculously when people who have grown up in the wizarding world to be be awed by anything other than particularly rare or complex magic. It's weird that the entire Weasley family stop breakfast to watch an owl flying in the window. Make the world a bit more lived in, please. One of my favourite details in Azkaban is the random extra reading 'A Brief History of Time' while absent-mindedly using magic to stir his tea.
Get Diagon Alley to ScaleIt's time to put some real thought into how this world works. JK Rowling likes to claim it was all thought out and planned prior to the first book being published, but this claim is at best a half-truth. Diagon Alley, as depicted in most media, is a single short street. We're also given the impression this is the primary shopping district, is not the only one, for wizards in London. We know wizards can distort geography. Let's make it bigger on the inside. The Ministry of Magic looks bigger than the entire Diagon Alley, which seems backwards. Get this world really built up.
The StaircasesThis ties into the earlier point about the style, but it's the one that most disappointed me when the movies came out. I never liked how mechanical the moving stairs moved in the movies, I'd rather they were more organic. Perhaps give them a bit of personality, have them sneakily move when people aren't paying attention or break the laws of physics.
Show Us the Quidditch World CupYou spent so much time setting it up...and you didn't show it. Film-making 101: it's a visual medium. Use visuals. It's a really great is way to establish the character of Krum. We got a weird version of the Barty Crouch encounter than is entirely meaningless since we don't have any idea who he is and it only comes back into the story some 2.5 hours later. If it's just for that encounter, have it take place at Diagon Alley, which doesn't need to be set up.
Set Things Up In GeneralThere are so many plot threads that the Harry Potter movies omit, which is fine. But you can't then include a pay-off further down the track if you haven't done the set-up. It's something the movies really should be called out on more. It's weird how much these films work off the assumption your read the books.
Dobby's death is something you feel should be a big, sad moment...but we haven't seen the creepy elf since the second movement. His entire story arc was cut out, but we're expected to have the same response to his death. Neville's hero moment and Malfoy's tragedy are both complete left turns without the time spent with them and their parents. Harry has Sirius' magic mirror in the 7th and 8th movies, but Sirius never gave it to him. Harry refers to his father and his friends by their nicknames without ever learning about these nicknames.
This goes beyond plot holes and continuity errors. This is sloppy.
Give Ron and Hermione Room to DevelopThere's a huge number of characters who didn't get the time they deserved in the movies, but Ron and Hermione are a special case as they share the screen with Harry Potter through the majority of the run time. Ron gets short-changed when many of his revelations and conversations go to Hermione. Explaining about 'mudbloods', often making a point to stand by Harry in times of danger, explaining about 'Beedle the Bard'...Ron is consistently dumbed down and left in the background.
Hermione, in the meantime, spends so much time delivering Ron's lines for him that she doesn't get some of her significant story lines dropped. The most noticeable cut has Hermione pioneer a (poorly received) civil rights movement on behalf of House Elves. It proves to a slightly more complex issue, but her determination and passion is key to her character.
Don't Get Too Caught Up in Book AccuracyYes, I've discussed some key omissions from the adaptations but ones that were half-assed or mishandled. Sometimes it's ok to leave things out. As long as you consider the long-term consequences and maintain consistency it's be fine.