Of course, we Catholics exempt revealed truth and the Church's teaching from being "open minded", since that comes form infallible authority, to which we have already submitted by a combined act of intellect and will ... assessing the Church's motives of credibility, and then making a submission of will and intellect.
Then there's everything outside of that.
So, the problem among Trads, the dogmatic types, has been to put stuff in the "keep an open mind" category into the "it's revealed by the Church" category, and that largely epitomizes the problem.
But for those types of things not taught by the Church as revealed by God, the key is to have some intellectual humility, where you admit you might be wrong and therefore are open to changing your mind, and ENGAGE IN SOME INTROSPECTION about your motives.
Since this video is from Dubay, let's take FE. I was initially dismissive of the entire notion, thinking that it was so much nonsense. Then in a moment of introspection I realized what I was doing, and then made an act of will to force myself to consider their arguments. I think it's nonsense, but I can't honestly dismiss it if I don't even understand or know their points, so, while I didn't expect to find much, I decided to go have a look and try to force myself to remain open minded. Well ... I realized that it was not anywhere near as dumb as I thought it would be. Even Dr. Sungenis admitted in an interview about his then-upcoming book about FE that Kolbe had asked him to refute FE, and he figured it would take about 10 pages, but then ended up in many hundred since, as he admitted, there's some fairly serious and signficant arguments that could be made for it.
Then once I saw their arguments and found them convincing, it still took me another year and a half to come around. So I did some further introspection. WHY am I so reluctant to simply agree that the evidence all favors FE and falsifies the globe? I realized that it was all the usual suspects, the psychological programming from childhood, where for over 50 years I had believed the globe on my teacher's desk and the styrofoam-ball model of the solar system I did for 2nd grade, reinforced with years of SciFi (that I enjoyed), working a few years for NASA ... and, probably most of all, knowing that I'd be subjected to ridicule, scorn, and derision if I publicly averred my belief that the earth is flat. Then, all that combined with the realization that I could be wrong, that I do not in fact have any direct proof, where I myself have gone up in a rocket and made observations myself ... that was difficult for me to overcome, and yet many here are stuck well short of that.
So, keep an open mind, and be intellectually honest, prepared to accept whatever conclusion the evidence leads you to, avoid the temptation to circle the wagons and defend your own tribal orthodoxy (Trads do this too ... I am with Kelly, I am with Jenkins, I am with Fellay, I am with Sanborn), and engage in some introspection about WHY you believe what you believe and why you might be resisting the opposite conclusion. What bothers you about it? If you are bothered by accepting a different conclusion, WHY? That will usually give you some clues.
Finally, I constantly engage in the thought experiment of pretending that I am an advocate of the OPPOSITE view, and try to formulate all the best arguments I can as if I were attempting to win a debate, without of course lying or gaslighting or any of that nonsense. If I raise the white flag, saying, "I can't honestly make a convincing case.", then I realize that my position was correct. Say, with evolution, I'm going to pretend that life evolve out of nothing and the big bang. I can't get half a sentence in trying to make a case FOR that because it's so utterly preposterous. I'd have to lie and gaslight. I've gotten to the same place with globe. There's nothing I can argue that I myself find convincing and not feeling practically guilty for being full of it. I can get into this mindset because in High Shool and Collegiate debate, most "seasons" had a single topic or two of discussion, and you had to be prepared to argue EITHER side of the topic, and I often felt guilty and dishonest doing it, and it's what some of the philosphers with some personal integrity denounced as Sophistry or Sophism. But, in a way, that's precisely what the Scholastic method is all about. See, St. Thomas, in raising his objections wasn't just putting up some strawmen that he could easily knock down, just to make his position seem more convincing. No, he thoughtfully considered all those alternative points, and the weaknesses and defects in those points actually led him to the current position he takes; they were part of his method for finding truth, and even Dubay hits upon that a little bit by using the technique of eliminating those things which cannot be true, i.e. you refute these objections.