Given the context (electron decaying to photon and neutrino), the lack of charge conservation isn’t wrong, per se, since you have to grant non-conservation even to get started. What left me underwhelmed was that he extends the standard model by introducing some new particles and couplings (fine), then snaps his fingers and says you don’t need charge conservation anymore, so his couplings are okay. The problem is that the standard model plus his extension must (mathematically) still conserve charge, so there is this Big Issue that he gets around by simply ignoring it (sort of by implicitly mumbling the equivalent of “oh, and, umm, pretend we have a way for my new coupling not to be mathematically inconsistent in the theory”… except he doesn’t actually even go this far; he just flat ignores the issue.)
Before the Planck time, I got nuthin’. After that, the idea is that you always make matter and antimatter in equal parts, so a zero charge situation becomes a (+1) + (-1) = 0 charge situation. The trouble with this is that we look around and see a matter-filled universe. The question of what happened to all the supposed primordial antimatter is a hot topic in cosmology and particle physics. No one knows the answer.
Looks like a Nobel Prize is guaranteed for whoever cracks the antimatter question. Are there currently any strong contending theories? Does string theory or loop quantum gravity, for example, offer any potential solutions to this problem or is it more fundamental even than that?
Eh, that’s not so bad, actually. The net charge of the Universe seems to be zero now, and before you had quarks and electrons, it was also zero. The problem isn’t so much with charge, but with lepton and baryon number: The zero charge in the Universe today is composed of a lot of negatively-charged leptons (i.e., electrons) and a lot of positively-charged baryons (protons), but almost no postive leptons or negative baryons.
That’s a less serious sin than violating charge conservation, though: If nothing else, gravitational interactions should be able to violate conservation of lepton and baryon numbers (a black hole doesn’t care whether it eats matter or antimatter), and most models for Grand Unification between the strong and electroweak forces also allow for non-conservation of baryon and lepton numbers. Presumably, conditions in the very early Universe were such that Grand Unification was relevant, so that provides the “how” of matter winning over antimatter. As for the “why”, there are some clues to that even in the unmodified Standard Model: There are some particle interactions which actually do subtly distinguish between particle and antiparticle, and it’s conceivable that, through similar processes, something in the conditions of the early Universe favored our type over the other.