A well-known bust of the Emperor Hadrian is prominently seen during the early dialog between Cassius and Brutus and, later, at Brutus' villa (both Cassius and Portia actually touch them). Hadrian wasn't Emperor for more than 120 years after the time in which the film takes place.
In the beginning of the film, when Flavius is talking to workers, we see Marullus near the wall behind, with a fat man a little way on his right side. The next shot shows the fat man partly behind Marullus.
When the soothsayer walks in the middle of the crowd to the right of the screen, we see from above when he is passing by Brutus. In the next shot he is walking towards the camera and Brutus, now behind him, grabs his arm to turn him.
Cassius offers Brutus his dagger to kill him, but the blade of his dagger falls off as he pulls it out of the sheath. Cassius offers the hilt of the dagger to Brutus, with the (missing) blade hidden behind his forearm.
When Decius Brutus comes to Caesar's home to bring him to the senate, Caesar tells Decius that his wife Calphurnia "on her knee hath begged that I will stay at home today." While this line of dialogue is verbatim from the play, in the film Calphurnia does not fall to her knees to beg Caesar, and instead remains standing, so this line of dialogue is inaccurate for Caesar to say in the context of this film.