I'm thinking his willful failure to be briefed by the CIA about Russian election tampering and not understanding diplomatic protocall.
Making off handed statements without proper research about the mater. He's an outsider when it comes to running the government that will make big mistakes at every turn because he seems clueless when it comes to running a government.
Those are not impeachable offenses. I think that his vice president and advisors will keep him afloat and clean up every mess he makes.
As for Republican politicians, they will tolerate Trump so long as they can manipulate him to their own interests. Without Republicans wanting to impeach him the process simply won't happen.