Is qada' (making up) or kaffarah (expiation) obligatory for someone who traveled two additional stops after paying for a monthly pass, thinking that was permissible?

Misinterpretation or not intending to cheat does not negate the rights of others. If the transportation card does not cover the two stations you used, you must pay their fare to the issuing authority of the card. This can be estimated by the price difference between the two types of cards.