From what I understand, he's accused Amazon of not collecting state sales tax on purchases. But it's been shown that Amazon collects state sales tax in every state that has one. He's accused the USPS of losing money on every package they deliver for Amazon. But the USPS and others have shown that the Post Office actually makes a lot of money off of Amazon, and have instituted Sunday deliveries in some areas because Amazon's business makes that profitable. He has claimed that Amazon has put a lot of brick-and-mortar stores out of business. But that same claim has been levied against Wal-Mart for years and while true to a certain extent is not any evidence of illegal activity. I really think it boils down to the fact that Bezos owns the Washington Post and Trump is trying to get back at him for that. Not one of the Presidents best moments if true.
Bezos has also stated a lot of liberal crap personally. Not just through his newspaper.
I think its no different than an actor or a sports person yapping their political opinions. Its out of place and inappropriate. They are no more important than anybody else.