Howard shatters Dominique's slightly damaged fireplace slab with a chisel and says, "Now it's broken and has to be replaced." When Dominique asks Howard if he can replace it, the next shot of Howard shows him kneeling in front of the not-yet shattered marble slab.
When Roark is having his first meeting with Toohey he has a copy of the Banner in his hand. When Roark says "I read that in your column yesterday" the paper in his hands is open. The scene shifts perspective to Roark from behind and the paper is folded.
When Wynand is in his office talking with Toohey (about 15 minutes in), the shot of the seated Wynand shows him looking at the bottom half of the front page of his newspaper. When the angle shifts to Toohey, Wynand is suddenly reading the top half of the front page.
When the Banner prints its front page story "The Truth about Howard Roark", a six-paragraph story is shown - but the first three paragraphs of the story are exactly the same as the last three paragraphs.
When Dominique is taking the construction elevator to the top of the skyscraper, the camera (as if from Dominique's perspective) zooms in slowly to the top of the building but there is no elevator shaft.
When Cameron smashes the window in Roark's office, you can see that the flag outside the window flying in the skyline is not rippling and therefore is part of a photographic backdrop rather than a live location.