[Jeffhs]

That the dot doesn't appear anymore shouldn't be a problem. In fact, it is probably just as well that you don't see that dot, as it could burn a small spot on the CRT phosphors. One way to eliminate the dot is to increase the brightness just a bit before turning the set off. This dot appeared on older TVs (it doesn't on later b&w sets and certainly not on flat screens, as the latter do not use CRTs) because the electron gun inside the CRT stayed hot enough for several minutes to create an electron beam after the set was shut off. As was mentioned, some TVs had a bleeder resistor that forced the CRT into cutoff just before the set was switched off, and some sets had an actual "spot killer" circuit using a relay that performed the same function.

I have never seen the dot on a color TV; don't know why. I would imagine, however, that this would appear as three separate dots on the CRT screen, since a delta-gun color tube has three guns, one for each primary color. Therefore, if the "dot" were to appear on a color set, you would see not one but three separate dots arranged in a triad in the center of the screen. I would also guess that most color sets had a spot killer system to eliminate these dots and, therefore, protect the CRT phosphors from burns.