Language issue

As you can see, the reality was that everyone might have had headphones available. https://www.ushmm.org/wlc/en/article.php?ModuleId=10007148

But if I were a German fluent in English as Herr Rolfe apparently was, I might have chosen to address the tribunal in English, because I would prefer that the judges hear my choice of words and not the translator's. That would mean the judges would not have to put on the headphones. Similarly, Dr. Janning might well have chosen English. I'll agree that the witnesses would likely have only spoken German.

I'd observe, however, that the presence of the simultaneous translation does seem to mitigate the use of English in the movie - the English speakers in the courtroom would have been hearing the testimony in English, just as the audience in the in the movie theater is hearing English.

Everyone wasn't speaking the same language. At least, not within the world of the film. All the characters are speaking their native languages - notice how whenever the prosecution or defence object to or interrupt the other's questioning, the other immediately puts on their headset and how, when Maximilien Schell's German character approaches Montgomery Clift's German character, he makes a point of telling him that he can take off his headset, whereas both Clift and Richard Widmark had both been wearing headsets prior to that because (in the context of the film) Widmark's character had been speaking in English and Clift's had been speaking German with each hearing a translated version of the other's speech. The fact that (out of the context of the film) they're all speaking English was purely for the benefit of the film's audience who would be more than likely primarily English-speaking. The film itself goes out of its way to make sure that we as the audience understand how the language in the film works with the first few minutes of the trial setting up that there are two primary languages being spoken (English and German) and interpreters are giving simultaneous translations via the headsets.

You also kind of have to remember that at the time this movie was made, subtitles were very rarely (if ever) used for any kind of sustained period in films. At most, you'd tend to have maybe one or two lines in a few scenes subtitled but certainly not whole swathes of conversation like you'd end up here if every character was constantly shown speaking their native language. Even if it were made nowadays I highly doubt they'd go the route of having subtitles through the majority of the film unless the production side of things was a lot more German-centric. The only other way would be to focus on the simultaneous translations being given by the interpreters but even then, having two people basically talking at once throughout the film would be quite a distracting experience.