In the beginning of tavern scene, the character of Michael Fassbender (center) wears bluish-grey cap, rest of the uniform being grey. Would that be a giveaway that he is a non-authentic German officer or it wouldn't be a big deal?
Screenshot: http://i.imgur.com/7U023RQ.jpg
The character in question is wearing a late-war field cap, conspicuous for the long brim. I'm not sure what you mean by overalls, but he's wearing an ordinary Waffen SS officer's tunic.
No, it would not be unusual for the cap and tunic to differ in shade. Most German army and W/SS uniforms came in a color called feldgrau - literally, field grey. Due to variations in dye, this could encompass a wide variety of grayish shades. This photo should make clear that field gray could mean everything from almost charcoal gray to olive drab to grey-blue. An officer might purchase his own uniform, made from higher grade cloth, but most junior officers probably didn't.