仕事で人の間違いを重視するあまり仕事が楽しくなくなった。 (At work, people focus too much on other's mistakes so work became unenjoyable.)
I think your interpretation in English is correct.
As for "あまり", I'll show you how it works by using the given phrase.
- 仕事で人の間違いを重視するので仕事が楽しくなくなった。
At work, people attach importance to other's mistakes, so work became unenjoyable.
- 仕事で人の間違いを重視するあまり仕事が楽しくなくなった。
At work, people attach too much importance to other's mistakes, so work became unenjoyable.
In other words, sentence 2 could be interpreted as:
- 仕事で人の間違いをあまりにも重視するので仕事が楽しくなくなった。
- 仕事で人の間違いを過剰{かじょう}に重視するので仕事が楽しくなくなった。
You can find a lot of examples here using あまり in the same meaning as the given phrase.
As for "重視{じゅうし}する", it is defined like:
to take something seriously; to attach importance.
There is a maxim in Japanese that is somewhat similar in meaning to the phrase you showed.
過{す}ぎたるは猶{なお}及{およ}ばざるが如{ごと}し
If I rewrite it in simple Japanese, it will be like:
多{おお}過{す}ぎることは足{た}らないことと同{おな}じようなものだ。
The maxim is interpreted in English like:
- less is more
- the last drop makes the cup run over
- too much of a good thing