Going through the list of assumptions on the 4th slide, I will list them in rough order of how much they are violated in real life.
- Perfect and Calorically Ideal Gas: No gas in real life is perfect, but in the throat flow this is especially true. The gas is at high temperature and pressure (often 1000s of K, 100atm, but very engine dependent), and step changes (See the freeze-out section in this link) in the specific heat are common place. This changes the isentropic exponent $\gamma$ with temperature. Furthermore, as the gas does not obey the ideal gas law, the equations for mass flow at sonic conditions are inaccurate even disregarding changes in the isentropic exponent.
- Constant Homogenous Chemical Composition: This would be treating the flow as Frozen. In real conditions, the engine flow is somewhere between frozen and equilibrium flow, where the chemical composition of the exhaust changes as the temperature and pressure change. Such processes almost always reduce the temperature in the combustion chamber and add temperature in the supersonic section of the nozzle. Depending on the assumptions about the chemical composition in the combustion chamber, the real engine can have higher or lower the mass flow.
- Flow is Isentropic: There is heat exchange with the walls (which is highest at the throat!) and conduction between layers of gas with different temperature. The flow is not isentropic. But to excellent approximation it may be treated as such. See this paper for a detailed treatment. (Sorry about paywall!)
- Flow velocity is axial: In the bell of the engine, this is obviously false. But in the throat, there are some nuances. Mainly, the boundary layer with the wall will affect the local choke point and velocity direction. But this is fairly minor.
- 1D Conditions: Similar to the above point, local BL conditions and anisotropic heating in the combustion chamber make this untrue, but again, extremely minor effect overall.
- Negligible Velocity in CC: Of course the velocity in the combustion chamber is non-zero. But its kinetic energy is extremely small compared to its thermal energy (Roughly a factor of $10^6$). Hence the $\approx$.
How the violations of the assumptions affect the mass flow at the throat will be dependent on how you used the assumptions (e.g. Frozen flow at exit conditions vs Frozen at CC conditions), the gases involved (reaction rate, specific heats, speeds of sound), engine shape and cooling method, and various other factors.
