Someone who made better use of rhetoric
One small benefit from the Trump phenomenon is better sensitivity to the same tricks, regardless of the speaker's tribal affiliation. I listened to a prominent speaker on my side of the environmental fence the other day, and was struck by how much he sounded like Trump, liberally interspersing his comments with "believe me," "I'm telling you" and similar. I'm not sure I would've noticed if it hadn't been for how often Trump would say those phrases, followed by outrageous assertions with no evidence to back it up. I eventually figured out that those words, "I'm telling you" are the support the speaker is giving for the factual assertion that follows.
So whenever you hear a speaker say "believe me" you are likely about to hear a conclusory assertion offered with no proof other than the credibility of the speaker. That's not always a bad thing - maybe the person's an expert and it's better to get many quick opinions rather than one deep backgrounder - but it's helpful to know that's all you're getting. And it's a rhetorical trick when used by a speaker you sympathize with - you think you've been told something and don't notice you've been offered no proof.
So, thanks Trump for the realization. In the case of my speaker, he was making predictions about the future, notoriously the hardest of predictions, based on "I'm telling you". I'm not giving it a lot of weight.
The other weird Trumpian rhetoric is saying we should ban Muslim immigration until we "figure out what is going on." What does that mean - could one possibly come up with a more vague metric for determining policy? What part of terrorism is Trump saying that we don't understand?
Of course someone could get a PhD in comparative studies of terrorism and not fully understand the subject, but that's not what Trump is talking about. This phrasing means to take vaguely formed fears and hate, or even a multitude of specifically formed fears and hate in the minds of listeners, and fit it all into something that pretends to be policy. As for "what's going on," Trump is letting people fill that void with whatever's in their minds, specific or vague, and think that Trump is saying the exact same thing. It's even trickier and more poisonous than figuring out what people want to hear and saying it back to them.
I'm sure it's been called out somewhere, but what's going on is cheap rhetorical manipulation.
UPDATE: thought I'd add that Trump also often appends "believe me" to the end of an assertion about something he's going to do or an outcome that's going to be achieved, when he'd have no legal ability to do what he claimed and the outcome is pie in the sky. Democratic presidential candidates aren't free of this either on climate change, talking way too much about policies that require repeated 60-vote majorities in the Senate and a majority in the House, but obviously there's no comparison.