The remarks that caused the most reaction and headlines had to do with Attorney General Jeff Sessions. Trump is still furious that Sessions recused himself from the Russian inquiry.
He is incapable of realizing that the recusal was legally and ethically mandatory. He is also incapable of understanding that the investigation now being conducted by Special Counsel Robert Mueller is legally and ethically mandatory.
As noted by The Washington Post (link here) in reaction to the interview: "The president asserted his prerogative to order an FBI director to end any investigation for any reason at any time." Trump, of course, is dead wrong with this. Both the Justice Department and the FBI are, as a matter of law, largely autonomous and beyond White House control for good reason.
Trump clearly expects his people to be loyal and do whatever they can do shut down any such investigations. He also vaguely threatened Mueller's team if they attempted to look at any of his business dealings, which a separate news reported indicated is now underway (details here).
The President clearly has no respect for the rule of law. He clearly thinks he's above the law, embracing the Nixon maxim that "whatever I do is legal," a policy which the Supreme Court long ago flatly said is wrong and not founded in the constitution.
One has to wonder if some of what Trump said in the interview could even be used in an obstruction of justice case against him. A US Senator from Connecticut and former federal prosecutor hinted as much when he tweeted (link here) "threatening the Mueller investigation is more evidence of obstruction of justice -- a criminal case unfolding in real time before our eyes."