1Weasley family in Egypt

Early in Harry Potter and the Prisoner of Azkaban, Harry sees a newspaper article with a photograph of the Weasley family in Egypt. Though it is never again mentioned in the movie, this is a very important plot point in the book. While on an inspection of Azkaban, the Minister of Magic had a copy of that paper, gave it to Sirius Black, who recognized that Peter Pettigrew was disguised as Scabbers. This is why he decided to break out of Azkaban, track down Scabbers at Hogwarts, and take his revenge by killing him.
2Hallows Symbol

In Harry Potter and the Goblet of Fire, in the scene with Dumbledore, Harry, and the Pensieve, there is a 3D model of what looks like Hallows Symbol which becomes an important symbol in Harry Potter and the Deathly Hallows. Though the final book was not yet written when this movie came out, J.K. Rowling had a lot of influence over the movie details and she added lots of objects and plots in the movies that were referenced later.
3Beauxbatons girls

In Harry Potter and the Goblet of Fire, when the contestants enter the arena for the third task, the Beauxbatons girls in the audience can be seen dancing the Macarena.
4Cereal brands

During the breakfast scene of the Great Hall in Harry Potter and the Order of the Phoenix, students can be seen eating parodies of real-world cereal brands with the names such as Cheeri-Owls and Pixie-Puffs, with color schemes similar to those of Cheerios and Sugar Puffs boxes, respectively.
5Prewett Brothers

In Harry Potter and the Order of the Phoenix, James Phelps and Oliver Phelps, who play Fred and George in the franchise, make a cameo appearance in the picture of the original Order of the Phoenix as their deceased uncles, Fabian and Gideon Prewett.
6Black family tree

In Harry Potter and the Order of the Phoenix, when Sirius joins Harry in the room with the Black family tree, to the lower left of the door is a Starbucks logo. The “siren” has been stylized to be in keeping with the decor of the room, but she is wearing a crown and holding both her fins aloft as in the Starbucks logo.
7Love Potion

In Harry Potter and the Half-Blood Prince, the smoke coming out of the love potion changes color to that of whatever Hermione is describing. The final scent that comes out of the potion is orange, as is Ron's hair. That's why Hermione lies saying that she smells “spearmint toothpaste” because she obviously doesn’t want to say “Ron’s hair” out loud. Also, after Harry arrives at the Burrow, Ron pokes Hermione’s lip and says she has toothpaste on it.
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8Tom Riddle Memory

In Harry Potter and the Half-Blood Prince, Dumbledore reaches for a Tom Riddle memory dated 1938. He tells Harry that this was the first time he met Tom, but to the left, there is a memory labeled Tom Riddle that is dated 1937. It is most likely someone else's memory relating to Riddle terrorizing two children in a cave at the seashore, which is described in detail in the book.
9Arthur Bowen

Arthur Bowen, the child actor that plays Harry's son Albus Severus Potter in the epilogue of the final movie, can be seen in Harry Potter and the Half-Blood Prince buying roasted chestnuts at a stand in the Diagon Alley.
10Snape vs McGonagall

In Harry Potter and the Deathly Hallows - Part 2, Professor Snape still helps the Order when he redirects McGonagall’s spells to knockout his fellow Death Eaters. He also takes their wands before he flies out the window to make sure they could no longer harm any students. In the books, there are no Death Eaters around him so it was a nice touch to add this detail to the movie.