I just finished watching "Three Godfathers" (1936) in its entirety on HBO Max. After the opening credits, the movie does look really good and much better than my 2010 WA DVD. I don't know if it's coming out on BD, but I was impressed as the opening credits deceived me.I didn't think that 1936 version of Three Godfathers was pristine at all.
The 1949 version "3 Godfathers" starring John Wayne is one of the films I watch every Christmas season. I'll compared the HBO Max stream to my iTunes HD digital to see if there are any improvements.
As to "The Man Who Came to Dinner" I will try to watch that movie in its entirety too. The first five minutes after the opening credits look really good to me, but to make sure I'll watch the entire movie.