Indeed, it does.
Not necessarily, but he makes them often enough that, at best, it suggests a carelessness and a willingness to be perceived as unintelligent. Most intelligent people I know would take the time to correct mistakes like that.
But to your point, I would argue that the content, rather than the spelling, of his comments is a much better indicator of his intelligence. And his content is arguably worse than his spelling.
It's a lot easier to become a billionaire when your dad is worth hundreds of millions and hands you his successful business and decades worth of political connections.
And his campaign and part of his wealth were both fueled by his ability to market himself, which he's obviously good at. But self-aggrandizement of that kind only works when people can't effectively evaluate the merits of your claims and your ongoing job performance. We don't have the financials for his businesses, so we don't know how successful they really are, and we can't compare his performance running the Trump Organization to the performance of anybody else, because nobody else has ever done it. But now that he's president, doing a job that requires something more than branding and making things pretty, and where the results are on stark display every day and able to be compared to several predecessors, he's failing miserably. It's obvious that he's extremely limited in his ability to adapt to new situations and engage on subjects outside of those he already knows.
I do think that many folks are inclined to go too far in proclaiming how not smart or not successful he's been. But he's also far from the stable genius that he and his fans wish to believe him to be.