While not purely political Washington and Thomas Paine had a major falling out over Paine's imprisonment and near execution by Robespierre in France. Paine felt betrayed after Washington's failure to assist him in that situation, going so far to accuse Washington of collusion.

He wrote an open letter, attacking Washington's character, after his eventual release which served to cut Paine off from popular society. You can read the letter here: http://quod.lib.umich.edu/e/ecco/004829307.0001.000/1:3?rgn=div1;view=fulltext

Also, though I don't know the details, there was some contention when Washington offered to refuse a Presidential salary in exchange for an expense account - such as he had during the Revolutionary War. Seems he had been exceptionally skilled at padding his books, and amassed a small fortune at the expense of Congress after the war. Congress quickly settled on a fixed Presidential salary. His books can be read here: http://memory.loc.gov/ammem/gwhtml/gwseries5.html