I have completed the game but when I go back to play more side misssions the game only lets me replay the raid on illusive man base and the final battle on earth. I have tried 3 times and have gotten 3 different endings, which is cool. but I want to play some more battles and such.
Many missions become locked at set points in the story. Once you reach those milestones, the only ways to replay the locked missions are to start a New Game + (as Steve V. mentioned), load a save prior to the milestones, or start a new level 1 character.
Take a look at this list to see where in the story each mission locks and unlocks for your next playthrough to make sure that you don't miss any!