1) Accounting: Accounting, today, is mostly the same as it was a century ago. Namely, from an engineer's perspective, it does not contain the notion of error, which is obviously essential. If you go look at, say, Coca-Cola's financial statements, you'll find a value for their brand defined to the second decimal point. I know one thing about that value: it is wrong. It should be X(+/- error at 99% confidence).
2) Governance: Communication between management and stockholders is limited to the annual meeting, complemented by the board of directors. This model is flawed, the board of directors band-aid is ineffective, and there's room for much much fine grained communication and hence better governance.
Since stock exchanges mandate over these aspects of listed organizations, there is space for innovation, hopefully attracting investors and guaranteeing the spread of the next generation of business governance.