Answer:
The thing he would probably dislike the most about today's U.S. government is the involvement in foreign wars including the Iraq and Afghanistan wars. This is because John Adams, while not strictly a pacifist, advocated peaceful resolution of conflicts, and disapproved of the excesses of war.
For example, during his presidency, he did build up the army and navy preparing for a possible war against France, but in the end he signed the Treaty of Mortefontaine, which prevented any further escalation.