Other than the need for the two devices to each be connected to the same Wi-Fi network and the non-obviousness of being able to use your phone for other things once you start casting, I find it generally seamless, bit again I'm an 'inmate in the asylum' :)
I think it's sort of like what the other reply was talking about. Thinking about getting something onto the TV by opening something on her phone and then hitting some buttons was confusing.
I started presenting it as a process where you take something on your phone and push it to the TV, and I think that helped.
Instead just tell them to watch something on their phone. Then press this button and it sends it over to the TV instead. End of instructions. This was what finally made it click for my mother.