For me it was the juxtaposition of apparently realistic descriptions of orbital mechanics with the half-arsed handwavy gibberish about biology.
Maybe it's because I know more about life sciences than physics and simply missed that the orbital bits were equally nonsensical, but at least they didn't manage to shatter by suspension of disbelief. But then some vague magical genetics and a brief mention of "yeah, they can eat algae" are used to solve a bunch of intractable problems - and both treated as being far less interesting than, as you say, pykrete!
Given the title of the book and the fact that the final third hinges on the biological bits, it felt incredibly lop-sided - like he'd spent all his research time playing with Kerbal Space Program and only got round to stitching the two parts of the book together on the night before the deadline.
The biology stuff seemed far-fetched but plausible-ish, which was kind of how I saw the physics bits: sure, that might work given infinite tensile strength metals.
And sociology / anthropology / linguistics? Eh, we can wedge some stuff in once the important parts are done.
I didn’t hate the book at all. It was otherwise fun to read. But man, those bits I mentioned really stuck in my head and I couldn’t un-see them once I started noticing. Like, imagine that literally every time you were in a bar or restaurant with TVs, at least one of them was showing a documentary of the American revolution. Wouldn’t that be odd? Well, apparently in 7000 AD people just can’t get enough of their own founding history lessons.
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.
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I jotted down these things that drove me nuts in Seveneves:
* Describes pykrete every time it’s mentioned, which is way too often.
* Say “light green arc” again.
* There’s always a TV tuned to the Epic.
* Spacers and Diggers speak the same language after 5,000 years of English-Russian hybridization?
* So much time spent explaining the different races, then absolutely nothing was done with it.
* Red vs blue space, then absolutely nothing was done with it.
* “Diggers” capitalized in first use, no lead-up.
* “Sonar Taxlaw”? Really? Her volume of the encyclopedia just happened to conveniently start with “sonar”?
* They just gave up on Mars sometime, I guess.
* Oh, look, a secret religion at the end because, why exactly?
* Diggers would not have been remotely like “rootstock” humans after evolving for 5,000 years in caves. Look how much we’ve changed since 3,000 BC.
I liked it, overall, but each of these yanked me out of my suspension of disbelief.