Black and Scholes
is simply a Markov process in continuous time. If you were to draw a continuous process you would do so without picking the pen up from the piece of paper.
4) No commissions are charged
Usually market participants do have to pay a commission to buy or sell options. Even floor traders pay some kind of fee, but it is usually very small. The fees that Individual investor's pay is more substantial and can often distort the output of the model.
5) Interest rates remain constant and known
The Black and Scholes model uses the risk-free rate to represent this constant and known rate. In reality there is no such thing as the risk-free rate, but the discount rate on U.S. Government Treasury Bills with 30 days left until maturity is usually used to represent it. During periods of rapidly changing interest rates, these 30 day rates are often subject to change, thereby violating one of the assumptions of the model.
6) Returns are lognormally distributed
This assumption suggests, returns on the underlying stock are normally distributed, which is reasonable for most assets that offer options.