The Spreading of the Wave Packet

One of the big problems for the wave interpretation of quantum mechanics is the spreading of the wave packet. Shroedinger did some very clever stuff with his equation to construct cases where a little packet of waves maintained its spatial integrity, most notably in the case of the harmonic oscillator. However, once the electron was propagating in free space, there was nothing he could do to keep his wave packets from spreading out. How was one to reconcile this with the obvious fact that an electron produced at point A was always observed to travel intact to point B?

This is a very puzzling question indeed, but I must ask: just exactly which experiments do we have where an electron is produced at point A and detected at point B? Just as I argued in an earlier essay that we have no pea shooters for photons, I don't believe we really have any pea shooters for electrons either. Oh, there are obviously devices which produce a constant stream of electrons; and the rate of production of these electrons can be slowed down, probably to any arbitrary extent. But isn't the appearance of single electrons still unpredictable? I do not believe we have any reliable method for producing a single electron at point A and detecting it at point B. So what is the problem with the spreading of the wave packet?

People say that you can actually see individual electrons in a cloud chamber. The traces are undoubtedly very compelling: yet they may not be what they seem. In 1927 (or 1929? could it have been that soon after the Schroedinger equation)  Nigel Mott published an analysis which showed that for a spherically propagating wave, the most probable observed ionizations would be those lying on a straight line: in other words, the straight-line rays of the cloud chambers were in fact just what you should expect for spherically-propagating waves generated according to Schroedinger's equation.

The common belief that we can actually see individual particles, whether photons or electrons, is with us at every turn. Even Feynmann is guilty of it when he talks about the photomultiplier tube: he says you can actually see individual photons, and they are indicated by the click of the detector. There is a video of him kicking around YouTube where he makes this point, and it strikes me that he is uncharacteristically agitated, for want of a better word, when he makes this argument. Is he showing his frustration because deep down he knows his reasoning is flawed?