Continuity mistake: After Riddle yells, "Stop! No!" Harry stabs the diary the 1st time. In the next shot, as Riddle stares at the hole in his chest, he drops Harry's wand and it bounces near the Sorting Hat (fullscreen edition). In Riddle's close-up he is in the same position, he still stares at the gaping hole in his chest and Harry's wand is again in his hand. (02:15:20)
Continuity mistake: In the scene where Harry is stabbing Tom Riddle's diary for the last time, he closes the book and we see a close up of its cover, covered in ink. In the next close-up of the diary its cover is clean, and a small blue dot (where the ink subsequently squirts from) is visible in the centre for Harry to aim the tooth at. (02:15:45)
Continuity mistake: There is a scene where Harry is talking to Ginny in the Chamber, and he is holding his arm right below the wound. In this shot Harry has blood on his hand. When Ginny notices the wound, Harry moves his hand up to cover it. Now his hand is spotless. In the very next shot, however, Harry has blood on his hand again. (02:16:30)
Continuity mistake: In the first overhead shot of Dumbledore's study as he presumably starts to discipline Harry and Ron the corner of the rug below lies flat and evenly under Fawkes' perch. However when Dumbledore stands up to hand Ron the letter for Azkaban the rug differs greatly, though it has not been touched. (02:17:55)
Continuity mistake: Dumbledore asks, "Why then did the Sorting Hat place you in Gryffindor?" and in this close-up the Sorting Hat sits on two books. In the next shot, as Harry answers, "Because I asked it to." The hat now sits on three books in this close-up. During this entire scene in Dumbledore's study, things including the Sorting Hat and lamp behind Dumbledore to his right, change position depending on camera angle. (02:18:00 - 02:20:20)
Continuity mistake: In the second to last scene when Dumbledore is talking to Harry and Ron, Ron's hair is a bit roughed and has a big cowlick. In the next shot, the cowlick is gone and both Ron and Harry's hair is neat. (02:18:20)
Continuity mistake: When Harry is cornered by the Basilisk the Basilisk is a foot away from his face, but when he reaches to his side to pick up the rock, the Basilisk is a metre (about a yard) away. (02:19:10)
Continuity mistake: In Dumbledore's study, when Harry is handed Godric Gryffindor's sword, in the close-up the name written down the length of the sword is clean, with blood stains only below the name. Yet in the previous and following shots, the blood stains are much closer to the hilt of the sword where the name is. (02:20:50)
Continuity mistake: When Lucius Malfoy charges into Dumbledore's study, in the overhead shot as he says, "So it's true. You have returned," the diary is visible and it barely has a shadow on the desk, yet in the next shot, a close-up of Dumbledore, the diary casts a long shadow. When Lucius leaves, Harry begins to ask, "Sir...," in the overhead shot, the diary sits at the top of Dumbledore's desk, yet in the next shot, a close-up of the diary, it sits close to the bottom. (02:21:35 - 02:24:00)
Continuity mistake: When Harry, Dumbledore, and Lucius Malfoy are in Dumbledore's office and Harry says he will be around to save the day, his face is clean. Later, when Harry gives Malfoy Tom Riddle's diary, his face is as grimy as it was in the Chamber. (02:23:25 - 02:24:25)
Continuity mistake: When Lucius Malfoy tries to curse Harry, Dobby stands directly in front of Harry and says, "You shall not harm Harry Potter!" In the side shot of Lucius Malfoy being thrown, Harry is behind Dobby to his right and the grass with its shadow is visible. Though, in the next back shot Harry stands behind Dobby to his left and the grass is again visible, but with no shadow. (02:25:30)
Continuity mistake: When Harry falls out of the car as he and Ron are flying above the train, his hand misses the door handle completely and he should have fallen clear to the bottom of the gorge. However, in the next shot and after, he is hanging onto the handle quite firmly.
Continuity mistake: While Harry is communicating with Riddle's diary, after the words "let me take you back fifty years ago" appear on the page, the ink pot's lid is open as the diary pages flip and Harry lifts the book, but in the shot from Harry's POV we see the ink pot lid closed, then the lid is open again when Harry's transported.
Continuity mistake: When Harry is in the Chamber of Secrets and has just killed the basilisk, you can see in three or four shots that Harry is still on top of Salazar Slytherin's head. Now when the basilisk falls down dead, Riddle looks upward in anger at Harry who should still be up there. However, in the shot immediately following, it shows Harry walking right next to the dead basilisk.
Continuity mistake: When Harry stabs the basilisk through the roof of the mouth, he pulls his arm out and the fang is not in his arm. Yet a few frames later it appears.
Continuity mistake: When Harry stabs the diary with the snake fang, the tip should be full of ink. However, there is no ink on the tip when it is on the floor.
Continuity mistake: Throughout the movie, when Ron and Harry are standing together their heights vary in wide shots and closeups.
Continuity mistake: At the end, when Lucius Malfoy is talking to Dumbledore, Malfoy has a couple strands of hair going down his cheek. Just after he says "Well, let us hope-" he turns his head and the hairs disappear.
Continuity mistake: At the Weasley kitchen table, Percy hands the Hogwarts letters to each of the twins. A few shots later, you see one of the twins again being handed the same letter, this time from a different angle.
Continuity mistake: When Harry stabs the diary, it is completely soaked in ink, but when Professor Dumbeldore shows it to him it is partially dry. I doubt that Harry had time to escape the chamber, try and wash off the ink, and go to Dumbeldore's office. We see that stabbing the diary renders it powerless, so it can't have soaked up all the ink.
Answer: Yes. It's a common occurrence in a lot of movies for actors to forget their original lines so they improvise something to help move the scene along and not break character. Tom did this because he forgot what his original line was.