Corruption: Accepting gifts from foreign governments

Trump's acceptance of the gift of a used Boeing 747-8 from Qatar for conversion to his Air Force One certainly presents the appearance of corruption. Had Qatar given the plane directly to Trump, it would have been a clear violation of the U.S. Constitution's emoluments clause, which prohibits all Federal office holders from accepting gifts of any kind whatever, from any King, Prince, or foreign State without authorization from Congress.
Trump skirted this by claiming that the 747 was a gift to the Department of Defense, and not to him; but he also publicly said that it would be decommissioned after his term and transferred to his presidential library.
That sounds more like it's a gift to him, and not to the United States.

The "free" 747 wasn't really cost free. It lacked the secure communications and self-defense systems required by an Air Force One. The cost of its 9 month upgrade is classified, and officially part of budget for the LGM-35 Sentinel missile project; the New York Times reported that an unexplained $934 million funds transfer from that project was used for the 747's upgrades. This is more than twice the 747's claimed $400 market value.

It's also not entirely clear that the 747 was actually a gift. At the time the U.S. Air Force officially accepted the 747 from Qatar, both CNN and the Baltimore Chroniclereported that Qatar actually intended to sell it to the Air Force. That said most recent news reports (and of course Donald Trump) now describe it as a gift rather than a sale.

An interesting aside to all this was Trump's use of an entirely different military transport to leave Ankara, Turkey following July's NATO summit meeting. He had used the new Air Force One to travel to the summit, but appeared to switch to the old Air Force One for the first leg of his return trip. It was later disclosed that he had actually used another military VIP transport, and the old Air Force One had in effect been a decoy. The multiple switches raised questions about whether the hastily converted Qatari 747 actually had all of the security and self-defense systems required by an Air Force One.