When Ryan and Kelsi sing the beginning of "Be With You" you can clearly see that they are both singing the lyric "Even if we're miles apart" even though you can only hear Ryan singing until "miles apart."
When Troy asks Gabriella to the prom on the school's roof, they waltz to "Can I Have This Dance". Throughout the musical number, the daylight switches back and forth from early morning sun to evening sunset several times, suggesting that the filmmakers spent all day shooting this scene and edited together the best bits, although clearly filmed at different times of day and causing a disjointed feel.
In the graduation dance scene when Chad drops the basketball and it rolls behind him, we quickly see Troy reach down and pick it up. In the next shot Troy is dancing with Gabriella and the ball is gone.
When Rocket Man comes off the bench, he is taking off his white warm up suit. While he runs to the huddle he is taking off his warm up jacket. When he gets to the huddle he is tossing his warm up jacket, but he warm up pants are also off.
(at around 1h 30 mins) Sharpay and her assistant were dancing on the stage. One of the guys on the right side of the screen was standing a little taller than the rest of the male crews. A second later, he was standing in the same height as everyone else.
In the final scene when Chad and Taylor come up to dance he has a basketball in his hands. When it gets knocked out of his hands Troy picks it up but a split second later it is not in Troy's hands anymore, and Troy has his hands around Gabriella.
At the beginning of the graduation ceremony scene all the students are seen standing as Troy gives his speech; in the next shots they are then seen sitting on white chairs and then when the final song starts it switches back to them standing, the chairs have disappeared.
During the "I Want It All" singing with Sharpay and Ryan (Before Ryan sang it in the play), Sharpay is seen wearing a white jacket (Towards the end) over her white dance outfit. As she enters the cafeteria-scenery again, the jacket disappears.
The drama teacher Ms. Darbus tells Troy to turn out the lights and to lock up. Any teacher would see that the student departed and see that the building was properly locked up. However, Ms. Darbus has great trust in Troy, and also knows his father works at the school. She trusts that Troy would lock up.
When Ryan joins Kelsi in the music room during "Be With You" he looks at a piece of sheet music before sitting down and playing the song on the piano. However, this sheet music shown is only a vocal score and has no piano chords written on it so there is no way Ryan would've known how to play the song.
The trees have full summer leaves at the party after the basketball game. The weather would be much colder on a night after a basketball game in Albuquerque, which would have taken place in January or February or March.