Think it just boils down to more Americans being a bunch of racist simpleton c*nts than not.
When President Obama was exploring his running for POTUS, David Axelrod wrote a brief for him in which he touched on the fact that the most influential person in politics at the time, George W Bush, would not be running. He saw this as an opportunity for Obama to step in and fill the void. People wanted something different.
This to say that it's really hard to really assess someone outside of his context and completely isolated from his contemporaries.
That said, I saw your other comment about not arguing this from a point of policy, etc. so I'm going to do my best to stick to the person as you requested.
If you're looking to understand why so many voted for him and why most likely more will vote for him next year, many of these people have the attitude 'When I hire a plumber, I don't really care if he's got dirty jeans or swears, what I care about is that my pipes don't leak when he leaves'. By many metrics people look at, they think he's doing OK, so who cares about the tweets.
So the fact that he's bombastic, prone to over-exaggerate, over-sell himself, boast, insult people etc. It doesn't bother people too much. His rhetorical style believe it or not is part of his appeal, he's not scripted, and while it doesn't have the polish of a Mitt Roomney, it comes accross as authentic, and people tend to go with that, even it means putting up with some obnoxious traits.
Someone on here made the point that it's a cultural thing and I'd say there's something to that. I came to the US for the first time 20 years ago, moved here for good 6 years ago, became a citizen, have been to about half the states. I understand equally why many Americans back him and will stick with him and why many find him horrifying.
I don't mind him, he's a brawler, I don't think Mitt Romney would have made it in real estate coming from Queens. He's had to fight, wheel and deal, make associations and connections, deal with unions, probably at some point with mod bosses - this has all most likely contributed to his personal style. And yeah I don't mind watching the odd Trump rally once a while, he's not the most fluid orator, can get off point and ramble a bit, true but most accept it's part of the character.
Your question does remain a good one, most of the coastal and urban elites are still trying to work it out, and for all their refinement, smarts and cultural awareness, I don't have too high hopes for them. Looking at anyone and thinking 'They're wrong, they know nothing, and they'd better off thinking like me' is never going to help understand someone else's thinking and motivations.