In the films, they never acknowledged Dumbledore's change of appearance.

Of course, Richard Harris died, but in a universe where you have spells and potions, Dumbledore's change of appearance could have been explained. "After the events of last year [Chamber of Secrets], and the current problem [Sirius Black's escape from Azkaban], Dumbledore decided he had to be stronger and more prepared for the threats. He applied himself a very complex mix of spells and difficult potions to have a younger and more energetic spirit". Something like that.

However, since later we see flashbacks, that go before Harris's appearance of Dumbledore, the timeline actually ends up like this, chronologically:

#1 Dumbledore visits Tom Riddle. [Michael Gambon] #2 An adolescent Tom Riddle speaks to Dumbledore after the Chamber was opened. [Richard Harris] #3 Snape pleads Dumbledore to protect the Potters. [Michael Gambon] #4 Voldemort kills the Potters; Dumbledore takes Harry to Privet Drive. [Richard Harris] #5 Dumbledore tells Snape that Voldemort killed Lily and James. [Michael Gambon] #6 Dumbledore goes to Karkaroff's trial. [Michael Gambon]. #7 At some point, a frog card of Dumbledore is made. [Richard Harris] #8 Dumbledore protects the Philosopher's Stone during Harry's first year. [Richard Harris] #9 Dumbledore deals with the Chamber of Secrets' reopening, during Harry's second year. [Richard Harris] #10 Dumbledore deals with Sirius Black's escape from Azkaban, and stays this way for the rest of his life. [Michael Gambon]

So as you can see, chronologically Dumbledore changed between one appearance and the other, (of course, two actors at the time) but you can always could explain this by saying, "Dumbledore has numerous times changed his appearance, when the circumstances were appropriate." Now, this would be feasible, except for the fact of points #3, #4, and #5, which were set probably in the same week/month, so changing from Gambon's to Harris' and then to Gambon's in a small period of time seems a little off.

I don't know what you think.