How to ignore a presenter's bad english?
So I'm a native English speaker, and I used to be kind of a snob about people whose spoken English was poor. I got over it. I remember the exact instant that I got over it, in fact. Here it is:

I was an undergraduate, and I visited a seminar on a subject that interested me but that I didn't know very much about.  The speaker at the seminar had an impenetrable Chinese accent, and I wasn't able to focus on the talk at all because I could barely understand him. "This is terrible," I thought. "No one can possibly be getting anything from this."

The talk ended and the speaker took questions. The first question was long, thoughtful, and detailed: the questioner was trying to related something from a slide early in the presentation to a slide from late in the presentation.  I did not understand the question because the gentleman who asked it had an impenetrable Polish accent.

After some back and forth, it became clear that the speaker thought the question was interesting but didn't know the answer.  But someone else in the audience did: a long, thoughtful answer that I did not understand because the answerer had an impenetrable Russian accent.

Then it hit me: everyone in the seminar room had just learned something interesting, except me, because I was distracted by being an English-language snob.  That was my problem, not theirs.

I eventually figured out to concentrate on what's maybe called "active listening": constantly rephrasing what the other person is saying into my own words, and inquiring occasionally whether I'm summarizing things correctly.
You might not like to interrupt someone with clarifying questions during a presentation.  Within reasonable limits, you should get over that --- if you're flummoxed about something, chances are that other people in the audience are confused about the same thing.
Active listening has helped me to deal with native English speakers just as much as with speakers of broken English, in fact. For instance, when you argue with someone, they have a lot more respect for you if you can correctly state their position before you take issue with it.

(The happy ending of the story is that the Russian and the Pole both ended up on my PhD committee --- good people, both of them, from whom I learned a great deal. No recollection of who the original seminar speaker was, though.)