Donald Trump is apparently not going to sell off his businesses and put his assets into a blind trust, as the Office of Government Ethics recommends and as every recent president has done. He isn't going to release his tax returns, breaking a custom that began with Richard Nixon.
That almost certainly is going to put him in violation of the clause of the Constitution forbidding anyone holding federal office to receive emoluments -- the dictionary definition is "a salary, fee or profit from employment" -- from foreign governments. He might also potentially be at risk under a 2012 law barring presidents (and other elected officials) from profiting from information obtained through their office.