The Chamber of SecretsEdit
In Harry Potter and the Chamber of Secrets, Harry finds and explores the Chamber of Secrets (canon) with Ron and Hermione. In HPMOR Chapter 14, Harry tells Professor McGonagall that it is obvious that he should not try to find it or explore it by himself if he discovered it. However, in Chapter 49, additional information on what he might find in the Chamber makes him temporarily change his mind.
In the canon (vol. 3), a key plot element is that Peter Pettigrew hid for years in animagus (canon) form as the Weasleys' rat after he betrayed the Potters to Voldemort (while Sirius Black (canon) is widely believed to have been the traitor and to have killed Pettigrew).
Chapter 78 mentions a second-year Beauxbatons (canon) student who brews Polyjuice and drinks it after it gets contaminated with cat hair, and then hides instead of going to the infirmary. This happens to Hermione in her 2nd year in the canon. In HPMOR, the girl suffers permanent damage.
The Potters' mottoEdit
In Chapter 96,
In Chapter 26, Professor Quirrell tells Harry that a sixth-year student cast a dark spell on another one without knowing what it did. Of this Harry says "I do not understand how anything with that small a brain could walk upright". In the canon, during his 6th year, Harry casts the spell Sectumsempra on Draco Malfoy without knowing what it does.