
The fundamental "correctness" of TeX/LaTeX is beyond question, as there are no alternatives for scientific work that comes even close in quality and performance (except for variants found on CTAN of course). In particular, your underlying assumption that a "modern application" is bound to be better is nonsense.
That's not entirely true. A lot of TeX/LaTeX is "correct", but the
fact that a TeX file can change the behaviour of the TeX parser is now widely considered to be bad design (in Knuth's defense, there were of course plenty of good reasons for this back when TeX got written). It is one
of the reasons why it is so hard to make a TeX-compatible system
without essentially being identical to TeX. Moreover, despite the
small size of the TeX source code, reimplementing it in something more
maintainable is a very tough job; the various "modules" are incredibly
tightly coupled together.
However, if you are a good LaTeX citizen, and don't attempt to write
complicated style files yourself, this of course hardly ever matters.
This restaurant was advertising breakfast any time. So I ordered french toast in the renaissance. - Steven Wright, comedian