Uneven spacing around ellipsis in $[A_1;\dotsc;A_n]$

It's not a "known problem" It is a pretty explicit design aim. The code for \dotsc has

\ifx\@let@token;\@ldots\,

that is it tests for a following ; and adds a thin space \,

Sadly I suspect the reasons for that choice are somewhat lost in time (unless Barbara appears with a rationale)

the behavior is inherited from ams-tex -- but there's a particular "understanding" in ams-tex that hasn't been inherited.

ams-tex assumes that \ldots will be used only in text, and then (quoting from internal documentation that is not distributed publicly)

In text, we want to ignore spaces before \dots, and we want to leave an extra thin space if the next token, which we get with a \futurelet, is a , or . or ; or : or ? or ! Otherwise (another letter or symbol comes next) we want to leave an ordinary space.

this can easily be demonstrated by processing this file with (plain) tex:

\input amstex
$$ A_1 ; \dots ; A_n \qquad A_1 ; \dotsc ; A_n \qquad A_1 ; \ldots ; A_n $$
\bye

the result inserts the thin space after \ldots as well as after \dotsc. \dots alone has the uniform spacing desired in this context.

alas, there's no documentation in amsmath.dtx regarding why this change was made.

a look into joy of tex, p.152, gives another hint: \dotsc is used in an example where the dots terminate a (mathematical) phrase:

Consider the infinite sequence $a_1, a_2, a_3,\dots$.

although in thi example the next thing is a period (end of sentence), it could as well be a semicolon (end of clause), in which case the extra thin space is desirable, and the recommendation ("the proper thing") "is to tell AMS-TeX which sort of dots it should be using:"

Consider the infinite sequence $a_1, a_2, a_3,\dotsc$.

for myself, i would use \dots rather than either \ldots or \dotsc, examining the output only to check whether i really should have used \cdots.