You don’t need rules to roleplay your character – this should not be random
Just roleplay. Think about what your character hears and how he might misinterpret. Think about some odd phrasings that he might use, as too-direct translations of his own language, using syntax and idioms that Common doesn’t. And use these. Stay in character, and be honest about when your character will misunderstand.
You don’t need dice, you don’t need skill ranks; this is not something best-handled mechanically. That’s because the rules are far too static to handle every different scenario, every different statement, and how likely you are to misunderstand. You, as a thinking human being, can say “ah, he’s heard this before and had it explained to him; he knows this,” when the dice would just say “aha, a natural-1!” That doesn’t add to the game.
Also, dice cannot decide to react differently, and it is going to be very important that you do. This kind of character requires you to exercise a fair amount of judgment about what does and does not improve the game. Done too much or at particularly bad times, it could seriously detract from others’ fun. As the Giant says in the linked article,
You are not your character, and your character is not a separate entity with reactions that you cannot control. I can't tell you how many times I've heard a player state that their character's actions are not under their control. Every decision your character makes is your decision first. It is possible and even preferable for you to craft a personality that is consistent but also accommodating of the characters the other players wish to play.
Note that I am not giving advice on when or how much, just that you should be in control of those things. It’s going to be very dependent on your group. Some groups will be very annoyed if their carefully laid plans are ruined by this “quirk,” while others will find that the height of hilarity and/or drama, and an awesome story they’ll tell for years. You have to know your group – and you can be very sure that the dice don’t know your group.
So have fun with it, but also be careful with it. Used appropriately, it will be a fun, funny, and memorable character. Used inappropriately, it will be annoying, derail the game, and quite possibly cause out-of-character disagreements when your “fun” misinterpretations prevent other players from getting on with what they want from the game.