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Typo at the end of $(b)$: there is a superfluous ")". Typo in the third diagram: $c_Y$ should probably be $c_{X', Y}$

Typos after listing the properties:

• "Writing $X$ as the filtered colimit of its finite simplicial subsets ..."
• "If $X=\emptyset$, then $c_X$ is an isomorphism ...": $c_X$ should read $c_{X,Y}$.

You also write: "... and also for $n=0$ because $\Delta^0$ is a retract of $\Delta^1$ ...", but never show/mention that retracts of good simplicial sets are good (maybe on purpose of course!).

Yep. Thanks!

Maybe typo at the end of ($c$): $v$ is an inner anodyne by virtue of Proposition 4.3.6.4.

Yep. Thanks!

noting that the upper and lower squares are categorical pushouts

I guess it "upper and lower" should be "back and front".

Yep. Thanks!