Let's run the numbers and see if the Heisenburg Uncertainty Principle is inconsistent with how a CRT works:
The equation is:
where the sigmas are the uncertainty in position and momentun, respectively. Given the mass of an electron and typical velocity from an electron gun of about 6x10^6 m/s, the momentum of the electron is:
The variability of velocity is probably around plus or minus 1%, given the variation in how electrons boil off a cathode and how accurately the voltage of the elctron gun is regulated. But for fun let's assume that the variability is held to a very high standard, say 0.01%. This means that the uncertainty of the electron's momentum is:
So from Heisenburg the uncertainty of the electron's position is:
This level of uncertainty in position of an electron is much, much smaller than the width of the electron beam hitting the CRT screen, so the Heisenburg Uncertainty Principle does not adversely affect the sharpness of the CRT display.