The plot is based on a true story which I didn't know anything about, so while watching it I found some of the scenarios far-fetched, although after I came home I checked and found the real story even more bizarre (according to Wikipedia, so take with a pinch of salt.) I'd actually like to see it again now, with the knowledge that it isn't "jumping the shark", and I could suspend my disbelief better!
I was happy with Angeline Jolie's performance in the lead, but was particularly impressed by John Malkovitch since he played a role that was outside his usual range (i.e. not evil or demented). Because he was an unusual casting choice for a good guy, I felt it added a certain depth that the character wouldn't have had otherwise. There were a couple of great scenes, such as the one at night-time in the chicken coop, which managed to convey the horror of the situation without just relying on gore; and the interview in the insane asylum which had its own horror. Thinking of it, they were both illustrating the impossibility of escape. One image that I found especially strong late in the film was a shot of Christine Collins grasping the bars of a prison door.
Something that I unequivacably liked was the colour scheme for the movie. The opening shot was a high-level city view in black and white, and then it came down to a street and picked up pigment. But the colours used throughout the film were the shades that were used to tint old postcards, and it really gave it a strong effect of the era.
And finally it passed the Bechdel Test which isn't something I search out films for, but is always a nice bonus.