Random misfire and code P0300

I have the vehicle listed above my boyfriend got it from one of his friends. It has a motor from a 2011 and it my question is the motor and exhaust that was originally in the car had the air injection system on it but the 2011 motor that they put in the car it did not have the air injection system. So with them leaving the exhaust manifold from the 2008 motor on to the 2011 motor will that cause it to have a random misfire? How much does that air injection system actually have to do with this? Is this why I'm having a problem because I got a code p0300 random misfire.