Minor plot hole: Workers of the Adjustment Bureau can create portals to various locations by turning doorknobs clockwise (with their magic hats). However, Matt Damon's character is able to create portals at the end of the movie while opening various doors with push-handles and/or levers that cannot turn in a clockwise position.
Plot contrivance: The antagonists of the movie, the caseworkers of the Adjustment Bureau have incredible powers. They use telekinetic abilities similar to Jedi, they can teleport almost anywhere and they can FREEZE PEOPLE instantly. But somehow, they are incapable of stopping 1 lonely man from running to a destination they already know, let it be a dance show or the top of a building.
Unaddressed Issue: Thomson, an authority of the Adjustment Bureau, explains that the agency let the humans decide their own fate from around 1900 to 1950. His point was that humans were too violent to be free-willed and thus required outside supervision in order to escape other catastrophes that were the two World Wars and the Great Depression.
This thus means that the Adjustment Bureau is working to help the United States of America only. Because part of The Chairman's plan involved centuries of slave trade, conquest, wars and genocides that were not part of American history.