He beat the assistant captain of 4th company and two others with his hands. Note that this was a very short time from just acquiring bankai and being healed in that spring that yoruichi has. In short, he was more prepared to fight than they were, and in the case of kotetsu, she was never gonna take him on and win >_>
As for his dad, when did he ever say his reiatsu didn't compare to ichigo's? He's never spoken much about his strength at all, or even released his zanpakuto at all. he sliced an arrancar in half with his unreleased sword. How the hell would ichigo match that right now? As for his powers, shinji and the other vaizards are all made out to be far more powerful than him, as well as having increased endurance and ability during the hollow transformation. Are any of them broken? >_>
The hypocrisy in my previous post isn't my fault - after all, I never designed ichigo. I'm merely stating my take on things. You don't need to be so defensive, nobody is gonna argue that ichigo's character isn't broken, that would be stupidity. But let's face it - clearly some of the captains ichigo fought in soul society were holding back - and even then he only really fought two of them. There's absolutely no indication that ichigo is stronger than ALL of them, merely that he has the potential to be even stronger.
Again, he IS broken. But he's the main character in a shonen jump manga. What are you expecting?