There seems to be a lot of buzz around the Internet that the now famous Roadster is going to overshoot mars. Was this intentional, just to show the kind of capacity it is capable of? Or was there some sort of miscalculation that caused them to burn for too long, or could there be other reasons for the overshoot?
It was entirely intentional to enter a solar orbit with an aphelion past Mars' orbit. There was never any intent to target Mars itself, since this is simply the wrong time in the synodic period to attempt that. It did not "overshoot Mars" since Mars isn't in the crosshairs here. The only objective was to show that the vehicle could deliver enough energy to the payload so that you could target Mars if you wanted to, in a proper opportunity.
The only miscalculation was in an image that Elon Musk tweeted that showed about the correct $C_3$, but also showed a miscalculated and way too large resulting aphelion. The correct aphelion is closer to 1.7 AU.