I've recently started a re-watch (as I'm sure many fans are at the moment), and I've found a new appreciation for Hartnell. The line fluffs grate occasionally but for the most part I found it quite refreshingly natural for a character on TV (especially an eccentric and forgetful old man) to fluff his words and lose his train of thought the way people actually DO in real life. Even when it's unintentional it ties in with him getting Ian's surname wrong and the like. He was supposed
to be doddery and comically forgetful, and I found it amusing to occasionally see the other actors smile in character at some of his fluffs. For me, it added to the character. I'd also contest that "No-one else, even the guest stars, have this problem"; not to the same degree, no, but the show was recorded 'as live', with retakes only being done if everything went completely tits-up, and several of the cast do occasionally fluff lines in those early stories. It's worth noting that the screen medium was very young at this point, and screen acting was far less naturalistic than it is today.
I also feel compelled to point out that Hartnell was not a well man at this time, and that his arteriosclerosis (of which he was suffering the onset) made it harder for him to remember lines and eventually contributed to his premature departure from the show. By all accounts, he would get very frustrated with himself and his inability to perform the role to his own satisfaction, and his resultant irascibility made him somewhat difficult to work with. In a way, while very sad for him (he was
a great actor in his day) it gave the show its longevity. If Hartnell had been well enough to continue, the show would have died with him, but the fact that ill health forced him to leave before time necessitated the invention of regeneration...
Patrick Troughton rightfully receives much praise for his portrayal of the Doctor, and for being the template for who the Doctor is now (he's certainly the most influential on his successors), but I think it's all there in Hartnell's performance too.