Regarding the "already seen it remark," I can't find any reference to Poirot and Hastings reading it– unless they saw it in the despatch-box, but my guess is that a reference to Miss Howard showing them the letter was deleted at some point in the editing process.
As for the "17th" letter, Miss Howard couldn't say that there was no letter (though she could've claimed it got lost in the mail) because Mr. Inglethorpe had probably heard through the investigation that Mrs. Inglethorpe had sent Miss Howard a letter that day (remember, that point was made publicly on at least one occasion, so everybody knew there was a "17th" letter). Based on the fact that Mrs. Inglethorpe found her husband's damning letter addressed to Miss Howard (and locked it away where he couldn't get to it), she probably wrote a letter to Miss Howard along the lines of "Dear Evelyn, What the heck is going on? I just found a letter my husband was writing to you? He thinks I'm going to be dead soon? What on earth did he mean about the bromides? Are the two of you having an affair? If you don't explain yourself very soon I'm going to call the police. Sincerely, Emily" Miss Howard certainly couldn't show the police that letter, and she'd heard from Alfred that the police knew about the "17th" letter. Only one thing to do. Burn the real "17th" letter because it could get her hanged, and then find a duplicate letter– and putting a "1" in front of the "7th" was the simplest and seemingly elegant solution.
Dr.Sheppard, you're right that Christie's name isn't as prominently mentioned as one would think it would be. Though Christie is mentioned lots of times in the various interviews and news articles, her name isn't on the teaser poster, although there is a "Based on the novel by Agatha Christie" line amongst the general credits of the teaser trailer. I'm not sure why "Agatha Christie" isn't featured more prominently.
Yes, thanks to everybody who responded! The Moving Fingeris one of three Christie books with very different US/UK editions. As P_Lombard states, Three Act Tragedy was also changed (the motive used in the David Suchet TV adaptation was the original one, whereas the motive used in the Peter Ustinov TV adaptation was the revised one, created for US audiences because of different laws in America, and a feeling that Americans wouldn't accept or understand the original motive). The other heavily abridged US edition is Murder is Easy, which, like Moving Finger, was substantially cut to save paper and for serial purposes.
Poirot seems to get along well with amiable, good-hearted (albeit slightly immature) young men– at times, he comments on Hastings' "childlike" demeanor. I think (SPOILERS) that there are other reasons why Poirot doesn't care so much for Franklin...