In Diablo II, it was possible to visit previous acts via the waypoint system. It appears that is impossible in Diablo III - how do I go back to previous Acts, so that I can get achievements and such from previous parts of the game?
Exit to the menu. On the character select screen, select "Change Quest". This will let you go back to any quests you've previously accomplished, but you'll lose your progress on the current quest.
It is possible. At character selection screen select the act you wish to go to from the quest selection drop down box. Should take you to the act you wish to go to!
You have to log out and then go to change quest to select the quest. Unfortunately, you can not switch acts in game.
With the release of the expansion Reaper of Souls you can use Adventure Mode to visit every act in game without going back to menu.
Although some achievements will require the game to be in certain state, to get them you will still have to use the option "change quest" and start in Campaign Mode.