I agree with Ineedacleaner a few pages back - the Ns and Ms look similar enough, from what I've seen, to be read as one another, so I'm not convinced that was actually a mistake at all.
However, I can also believe that, given the serviceman's name - Jamie Janes - he may have accidentally got the N and M confused when reaching the surname. As someone has said, with a name like this it must happen a lot. And if that's what happened, it's entirely possible that he could read it through and not notice because the eye will show you what it expects to see half the time in that situation.
All that aside, even assuming it was an error, I am with the OP and many other posters here in feeling that this has been deliberately blown up into a supposed huge 'insult', in a way that does no credit to Mrs Janes (though I am sorry for her loss of her son, I don't think this way of handling it will do her any good in the long run) or to the Sun, and the rest of the media who have picked up the story and run with it. It also makes me feel sorry for GB - I'm not much in sympathy with him at the moment, but he could not have done right for doing wrong on this issue. A typed letter would have been scorned by his critics as impersonal and done by a lackey. Personally I would rather my Prime Minister had other skills than good handwriting (and agan, the question of whether GB has those is another matter and not relevant here).
I don't see how any letter could compensate Mrs Janes for her son's death, but the one sent was a genuine attempt to give comfort and show respect. I also wonder whether Mrs Janes, or the Sun writers involved, can honestly say they have never made a mistake or got wrong an aspect of something they were doing for all the right reasons - or, come to that, whether they all hae perfect handwriting and always get people's names right.
I am not from a military family but I strongly believe in supporting our servicepeople; however, I think in this case that banner is being badly misused to veil cheap political point scoring.