Dialogue

They did not modernize the dialogue at all in this film, but trust me when I say that is no obstacle to understanding every word in it.

I did not like Shakespeare much in school, but it was this very 1953 version that got me hooked when I saw it on television a decade later, mostly because I found myself understanding the dialogue without having to try. It even came as a shock to me while watching it, with a sudden "HEY!! I UNDERSTOOD WHAT HE SAID!!" :)

I got lucky by having it be Julius Caesar, because of all of Shakespeare's plays it has been generally accepted (at least in previous generations) that Julius Caesar has the most accessible dialogue. This is especially true when seeing it performed instead of read, even moreso with this particular film. To read Brutus saying "how ill this taper burns" might need endnotes, but to see James Mason look at the flickering flame clears it up. What shocked me was not only that I was suddenly understanding the language, I was starting to appreciate it. I thought "What a COOL way to say 'the candle is flickering.'"
Or Casca saying "if your mind hold." "Wow, what a great way to say 'if you remember.'" And he says it with such matter-of-fact ease that it just starts to sink in as you watch it.

The Heston version didn't modernize either, but I don't recommend it over this 1953 version. Heston was fine as Antony, but Jason Robards was awful as Brutus. For some inexplicable reason he talked in an emotionless monotone throughout most of the film.

You can read the play for the understanding, the history and plot, the poetry - even subplot and comments on the religious strife of the era some say. You can see the word, man, as interjection, and 'right on' actually used if I'm not mistaken.

But the phrasing and delivery are important. And I have never seen Anthony's funeral oration delivered more convincingly than by Brando. It's said that he had Gielgud deliver his version, as inspiration. Gielgud of course plays Caius Cassius. But in listening to what he says, the words make sense. The inversion of words to fit the iambic pentameter don't bog anything down. You wonder if much the same was delivered when this was played originally in England, or how influential these plays, particularly Caesar, might have been in Elizabethan England.

It's certainly the case, though, that his plays have been altered repeatedly for stage and screen. Olivier seemed not to mind at all, and I'm sure found it useful to do so. I'm sure Brannagh never minded that, either.

You could simply extrapolate, perhaps, the performance to those lines which were removed, or even altered. Of course, anticipating what Brando might have done in this case or that is problematic. Perhaps it's best to imagine your own characters, after such inspiration, and follow them as you would imagine your own sense of characters in any play, any novel, frankly most any historical account.