The limit formatting the author doesn’t like isn’t a bug in pandoc I don’t think - it looks to me as if they have just written it ambiguously in latex.

If you write a limit as \lim_{n \to \infty} etc etc then LaTex gets to decide whether to write your limit in inline style (next to the limit) or below. If you want it always to be below then you need to write

\lim\limits_{n \to \infty}

It’s the same deal with summations and integrals.