I believe that repeated cloning would cause physical issues as well, but that's not something that would actually have an in-game mechanic. I think it'd be safe enough, however, to say that the more you're cloned, the more likely you'll have problems with your genome, potentially causing mental and physical problems ranging from... Well, anything. Your genetic code is literally who you are. Changes in hair/eye color, skin, problems with any and every process your body conducts. Digestion, breathing, movement, personality, changes in taste, anything.
But being cloned once or twice in a short timeframe isn't likely to do anything. I don't think there would be any REAL problems until the fourth clone. This is something that'd go in lore, but is one of those things that doesn't have a mechanic, if it's to be implemented at all.