I notice that the name of one of the second unit directors on Indiana Jones and the Last Crusade is "Michael Moore". Is this the same Michael Moore who became the famous documentary director?
That was a different Michael Moore (Mickey Moore, Michael D. Moore), born Dennis Michael Sheffield (1914 to 2013).
From his wikipedia page:
In the 1980s, Steven Spielberg hired Moore as second unit director on Raiders of the Lost Ark, Indiana Jones and the Temple of Doom, and Indiana Jones and the Last Crusade.
His obituary in the LA Times also mentions his work on the first three Indiana Jones movies. And a link to his IMDb page ("Second Unit Director or Assistant Director") listing the first three Indiana Jones movies.
The Director's Guild of America (DGA) has clips of Micky Moore from an interview with Duwayne Dunham. You can also search them for key words like "Indiana Jones". There's even a transcript below. Some snippets:
Chapter 2, Clip 4:
INT: Does Micky Moore have a style as a Second Unit Director, composing shots and action? Or does Micky try to match the vision of the Director of the first unit?
MM: I would say definitely try to match it to the first unit because that’s what you’re there for. You’re there to get footage that isn’t my thinking. It’s my thinking, it’s my problem to get the shots that look like whoever the First Unit Director was, his work. Yes, I think it was that.
INT: And do, in determining that vision, do you have conversation and/or refer to those storyboards? Are they real important at that point?
MM: Yes, because he knows what I’m doing and I know what he’s doing. And it’s like some of the, some of my shots are very difficult and the first unit would take too much time making them. It’s like all the shots with the tank with Indy [Indiana Jones] riding along side of it. We had a lot of problems because in the hurry to get the picture underway, they didn’t work on the tank the way it should be, and I couldn’t get it to make sharp turns and things. And I had Vic Armstrong doubling Harrison [Harrison Ford], and when you get the horse galloping and the tank, the horse always passed up the tank, so it was a hard thing to get the two together. Only that Vic was a good stunt double, he knew riding, he knew how to pull it in, that I didn’t have to photograph it that way. But we’ve got everything. It was interesting.
Here's the scene from Indiana Jones and the Last Crusade, Indy chasing the tank:
There's no indication that the other Michael Moore worked as a Second Unit Director. He was working as a journalist in the 1980s, before he was fired. In May 1989, Indiana Jones and the Last Crusade opened in theaters. In December 1989, Moore released his documentary Roger & Me about GM closing auto plants in Flint, Michigan. According to him, this story was also the reason for having been fired from his job as a journalist. That documentary was "financed partly by Moore's mortgaging of his home and partly by the settlement money from a lawsuit he filed against Mother Jones for wrongful termination".