1. There was no funeral for Dumbledore. In the novel, Centaurs and Merfolk all pay homage to the fallen wizard.  In the prior novels, a relationship between Dumbledore and these creatures have been established, but not so in the films.  The movie is currently just under three hours, and to tack on a funeral scene could push it over the three hour mark.  There was no funeral, but all the students raised their wands that eliminate the dark mark hanging in the sky.  The right music accompanies this scene.  A funeral scene is rumored for the next film, but Dumbledore still got the send off he deserved in this one.
2. There were too few memories scenes regarding Voldemort’s past. In the novel readers are treated to see Voldemort’s mother and family before he was even born.  They go on to learn of his life right after Hogwarts up to applying for the position of Defense against the Dark Arts (and the curse that befell that position when Dumbledore turned him down).  The film does provide movie audiences with the vital information they need to set up the next film with an exception.  Harry does not learn of Valdemort’s obsession with certain treasures from the founder’s of Hogwarts.  As far as he knows a Horcrux can be ANYTHING.  This issue will have to be addressed in the next film.
3. The Dursley’s were absent. They always provide some comic fun for the movies, but their presence was not needed to get this film moving.
4. Very little time was spent in the Weasley’s joke shop. It is established in the book that Harry provided the funds to Fred and George to open their joke shop.  That does not happen in the movies.  While any Harry Potter fan would love the film to spend more time in the famed joke shop it is time that is not needed for the film to work.  The black smoke and love potions are introduced and it is the only elements that are needed for the plot.
5. The new Minister of Magic is not introduced. Again, the introduction of Rufus Scrimgeour is not needed to move the plot of Harry Potter 6 forward.
6. Harry is not hiding under the invisibility cloak in the tower scene. Instead Harry is down one level looking up on the action on Dumbledore’s orders.  He does not take any action to save Dumbledore when he is killed by Snape.  The scene unfolds in a way that Snape’s actions completely take Harry by surprise.  There was nothing he can do.  How this hits Harry as far whatever guilt he may have will unfold in the next film.
7. There is no attack on Hogwarts and battle between the Aurors and the Death Eaters. This turns out to be a major plot hole in the film.  The reason why there was no battle, according to director David Yates, is that since there is a battle in the next film (Part TWO of the next film), they didn’t want to make it feel the series was repeating itself.  That is all well and good, but now Draco fixing the cabinet so the Death Eaters can invade the school makes no sense.  His ONLY mission is the kill Dumbledore and if he can’t then Snape must since he made the unbreakable bond.  There doesn’t seem to be any reason why they have to be there.  Could it be to make sure Draco carries out his mission?  Perhaps, but it is a weak  David Yates left plot holes in “Harry Potter and the Order of the Phoenix”, his first feature film.  This is the biggest one he leaves in this one.
8. The Death Eaters attack and destroy the Burrows, the home of the Weasley’s. Since books six does not have that many action sequences aside for the attack on Hogwarts, the filmmakers added this scene to help compensate.  Since the scene does not appear in the book the audience does not know what will happen.  Something the fans don’t get too much of in the films.  The scene does provide a good level of excitement and helps solidify the pending relationship between Harry and Ginny.  While it is not known, one can speculate that there will be no wedding scene in the next movie.  Charlie Weasley has never been introduced on screen, nor any mention of his pending nuptials.  Since the Burrows have been destroyed audiences do not need to expect an upcoming wedding.
9. The relationship between Harry and the Half-Blood Prince is diluted in the film. Harry has the positive relationship he has with Slughorn, in part, to the text book he possesses.  Once he hurts Draco Malfoy he has Ginny hide the book on him where they share their first kiss.  When Harry is chasing after Snape and tries using the same spell on hi he used on Malfoy it is then revealed that Snape is the prince.  It is almost thrown in as an afterthought and certainly could have been brought about in a better way.  What is also missing from that scene is how Snape is almost trying to teach Harry a lesson on how he must keep his mind closed or any wizard worth anything will know what he is about to cast.
10. Too much time was spent on the romance aspect of the film. While true, many of these scenes really let the actors flex some of their acting muscles in ways they have not been able to in the prior films.  It’s worth it.

The list can go on and on (Harry learning he inherited Sirius home, appration lessons), but these most of these are not needed to move the plot forward or can be addressed in the next film.  One can also look at these films as a whole and ask if they work if the books had never existed.  For the most part, the film stands on its own quite well.