Today, Washington would be investigated for inappropriate conduct and for accepting bribes. Today, in order to be a politician, a person has to be rich. Then they only get richer while they are in office, for no good reason. This conduct would be seen as taking money in order to have political access. Although, that's exactly what Clinton has done as Secretary of State and no one seems to care.
Yes, he would be investigated for unethical conduct today because it seems that every little thing will cause an investigation in this election. If Washington were running against Trump, Washington would be treated the same way as Clinton has been treated. Trump seems to get all of the investigations against his opponent.
Yes, it seems like just about any candidate today is being investigated and scrutinized over everything. It would not surprise me in the least bit if George Washington was investigated too for borrowing money to travel to New York. Who did he borrow from? Is there a conflict of interest? The questions would be flying.
Borrowing money to travel to be inaugurated is clearly not unethical. That is rediculous. He should not have needed to borrow money, but traveling was very expensive in those days, and he must have been broke. Now presidents make so much money that it would be unheard of for something like this to happen.