FTL communication? Eh, there's both enough new stuff to discover in physics and it provides such a massive boost to most stories that I'm generally willing to allow it, if treated well.
The clone personalities diverging almost immediately? Kinda torn. On the one hand, I think they would diverge significantly eventually anyway (take anyone at age 40 and give them a couple hundred years of experience being a martial protector, trying to unite nations, an R&D head, or a explorer of the wondrous, and you're bound to come out the other side with large differences), so I'm not sure how important it was to have it immediately if the plot points it helped could have been achieved in some other manner.
Edit: Added "around here" - which is quite important.... ;-)
The ostensible explanation for the later casimir generators was that they were pulling energy from vacuum fluctuations in a similar way that armature-linked buoys can generate power from ocean waves, but they were pretty vague on how that could provide more than a minuscule amount of power. Instead it was portrayed as being able to supply orders of magnitude more energy than fusion, which seems implausible. But at that point we're like 2 books in and already pretty invested...