I think Bert might actually be an INFP or an ISFP, even though it doesn't seem that way (given that Dick Van Dyke is about as E as it comes). He's incredibly strong in his feelings, and has the sort of grip on them that an Fi dom does - he takes both the good and the bad in their fullest, while remaining in control of who he is as a person. He's very wise, particularly given his lack of education, and he accurately diagnoses why Mr. Banks holds so steadily fast to his desires for order and precision with just a bare minimum of information. He then counsels George on the need to reconnect with his children: his heroics come through the use of Fi. I lean more toward INFP for two reasons - one, the absolute disregard he shows toward social class, and two, he argues using FeNi, subverting George's status issues to get his point across.
Now that I think about it, you're right on George being an ISTJ - his character development is through re-embracing his childlike Fi, and ability to connect with his kids as a result. Winifred is a particularly Edwardian ENFP, however, I could see her as ENTP as well. Now that I think about it, George could very well be a depressed INTJ, too - becoming rigid and unfeeling as a result of his almost-certainly harsh upbringing. He's stuck in an inferior-Se need to see external success and propriety, and deny the magic of the world seen through Ni. The play version is definitely a depressed ENFP: once idealistic, now stuck in his fine cage.
Also, just had a realization - given that the story is set in 1910, and that George is most likely in his early 30s at the time of the story, he'd have potentially been drafted six years (when conscription started) later to fight in the Great War. Thus, the whole theme of "be with your children, because time's running out" becomes even more acute. That's also in addition to the kids likely being sent to boarding school soon thereafter, which means that he would hardly see them in those ensuing six years.
