Zach Phillips explains my most significant frustration with iMessage on the iPad and Mac:
It would only take one feature to make Messages on iPad and Messages.app useful. Allow me to use my phone number as my iMessages account. My phone number has always been my unique identifier through which I choose to receive these short bits of text (for good reason). If I can't use my real “address,” there's not much point in signing up for a different delivery company. The package will not arrive where I need it.
Since iOS 5 launched, it has puzzled me why Apple designed the system so that iMessages sent to my Apple ID go to my Mac, iPhone and iPad while iMessages sent using my phone number only go to my iPhone. It creates a confusing (and technologically needless) situation where one ideally needs to give up iMessages' brilliant capability of seemlessly replacing SMS to reap all the benefits of using it.
Apple should fix this in iOS 6.