In the Past Lives Pavilion, as the subjects walk to their viewing booths, the overhead asks them to proceed to the "first available booth on the left." The subjects actually proceed to the last available booth.
After Daniel's 'trial' is completed and he and Bob Diamond go back to Bob's office where Bob is handed an envelope with the judgment, the envelope is clearly unsealed when it is handed to Bob, yet in his office Bob tears open a sealed envelope.
In the Italian restaurant scene, when Daniel asks Julia to turn back around so that Lena wouldn't see her sucking in the long strand of pasta, there is a split second where the strand can be seen falling out of Julia's mouth, but it remains in her mouth in the very next shot when she's facing Daniel again.
In the Past Lives Pavillion, it is shown that one of Julia's past lives was Prince Valiant. This would mean when Prince Valiant died, the judges determined he did not overcome his fears because he was reincarnated back on Earth and not sent on to the next phase of existence.
One the day of his 39th birthday (and fatal car accident), Daniel say that in 2 more months he will have worked at the firm for 10 years. However, Lena shows Daniel taking the job at 4 months after his 29th birthday, not 2 months.