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...
His early short stories have a lot of "drugs can let your brain talk to other dimensions" and "your mind literally makes reality" (though some of those are also really good, "The Infinite Assassin" is a great read and it's only like 15 pages), but his later full books are basically all hard (if speculative) physics stuff.
Dichronauts is difficult to get your head around, but very rewarding. It's about cartographers who work in a universe with essentially 2.5 dimensions of space and 1.5 dimensions of time.
The Orthogonal trilogy is about a species living in a toroidal universe where all 4 dimensions are identical and interchangeable.
The universes of Diaspora, Schild's Ladder, and Incandescence are set in a future when most intelligent life in the galaxy lives in a network of space-computers and interact with the outside world via robots and programmable matter.
Oh and I almost forgot the Bobiverse series. Not by Egan, but still good. Some guy gets stuck in a brain-computer and sent off in a self-replicating space probe to prepare other planets for human colonization.