The Letter (spoilers)

No, I think the consensus among critics of this film is that the content of the letter was a misjudgement. To leave it private, as in the book, is much better.

I actually agree with you. Having just seen the movie myself, I felt the letter to be very inappropriate for the actual scene itself. The letter went over what everyone was ultimately saying in their own head, and that the viewer – as I feel it – was intended to comprehend and feel as well. It is almost as if they wanted to spell it out for the viewer in case they didn’t catch it in the first place. Very unnecessary as far as I am concerned, and very strange to write your own wife given it will be the last thing she will ever read that would have come from you.
Regardless, I think his protest to the letter being read by the mob was in earnest. He knew that nothing he did or said would appeal to this mob. If I do recall, he was even quoted with saying that he knew their minds were made up before he even opened his mouth to explain his story. He had accepted his own fate ultimately. I think it was, for the most part, just the desire to keep his final (written) thoughts private as he had believed he had requested.
I think the intent (aside assisting the viewer to better understand what just happened if they didn’t get it) was for his wife to understand why it had happened. I highly doubt how it could possibly console her loss and I personally would have said something different. Maybe he felt that she might feel the need for a blind-justice vendetta the same way the mob had done onto her husband and he wished to avoid that if at all possible. Believing that by explaining this in brief, he can somehow avoid any potential problems on her end. Then again, when faced with death in that circumstance, one has a tendency to be all over the place mentally.

I agree.

I agree, I watched the film for the first time tonight and thought it was almost perfect. The one flaw was that letter. I didn't like having the message of the film read to me so to speak. I think we got the message without that.

I don't know.
I think if I was angry and about to die and only had a few minutes to get a few things off my chest and my executioners wouldn't listen to reason I would just start writing down whatever was on my mind. And being that angry and frustrated with the sudden unjust removal of all hope, I would have a word or two to say about what was happening to me and how I felt about it. It might come off as preachy in a movie, but I don't think I would especially care about the dramatic effect while I was spilling my last few thoughts on Earth. I would hope that my kids could have a chance to know some aspect of their father, so I wouldn't bother to reason what was appropriate for a husband or a father who was simply away from home. I would write the best thing I could under the circumstances, and I would do it with a sense of posterity.

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The shot of Henry Fonda reading the letter, with his eyes obscured by Harry Morgan's hat, is probably the most iconic scene in the movie. But I didn't think the content of the letter seemed believable for what a dying man would send to his wife.