Did anyone notice that the sorting ceremony wasn't in the movie? This is supposed to be the time the Sorting Hat's song tells all about the history of Hogwarts and also it's warning to stick together. But they went straight to the feast and spent all that wasted time on Umbridge.
I would have dearly liked to have seen the Sorting Hat, seeing as it wasn't in movie three or movie four. Harry wasn't present for the sorting ceremonies of books 6 and 7, so unless they make some deep changes, it is unlikely we will see any more sorting ceremonies. Did they film the sorting hat's new song? Apparently a lot of deleted footage didn't make it to the DVD. Offf the top of my head, here's a list:

Lily and James'a conversation in Snape's memories
Bellatrix dueling Sirius
Ginny and Harry watching the shelves fall like dominoes at the department of mysteries
McGonagall reading the prophet
Bellatrix stunning Tonks, whose hair turns white with pain
Lucius at his manor
Harry with bruises on his face

Also set reports confirmed that scenes where Harry skips stones across the lake (probably that last one), Hagrid introducing his fifth year class to the thestrals and McGonagall being hit by stunning spells were filmed. So was the hat?

Suppose that the people involved took not so much time reading the book ( or perhaps they did), but didn't see those things as "necessary". Always a budget has to be met and perhaps these scenes didn't fit the budget. That's just my little stab in the dark there.

General Ironbeak
The Sorting Hat is not an essential part of any of the stories, as far as exposition it feeds small snippets of information that are further explored in the future by another scene or moment. As such, it served it's purpose in the first two films which was to sort the students, and then to discuss his decision later with Harry. It is the first thing to notice Harry's link to Voldemort (the part of the soul lodged within him), hinted at through his belief Harry would have done well in Slytherin, and having revealed that information it has lsot it's purpose further on.
That is not to say that it isn't used well in the books, quite the contrary in fact, but in a film time is money and having the Sorting Hat sing isn't a priority, and needn't be.
The other scenes I can't confirm, and they are irrelevant really to your first question, but presumably if they were filmed they will turn up in the Extended Ultimate Editions soon to be hitting our screens. I myself am of the belief that the Snape's Worst Memory scene will find itself in Deathly Hallows in The Prince's Tale, if it makes the cut.

Well, I think it is probably still in the Hogwarts.The Sorting Hat is not an essential part of any of the stories, as far as exposition it feeds small snippets of information that are further explored in the future by another scene or moment. As such, it served it's purpose in the first two films which was to sort the students, and then to discuss his decision later with Harry. It is the first thing to notice Harry's link to Voldemort (the part of the soul lodged within him), hinted at through his belief Harry would have done well in Slytherin.