A Japanese person would have corrected this mistake.
If a Japanese person were involved in the business, he or she wouldn't have allowed that kind of mistake.
If there was a Japanese person involved, this kind of mistake would never have happened.
英訳① 「日本人ならこの間違いを修正しただろう」
「～なら…だっただろう」という仮定の話をしているので、仮定法過去のwould have done が使われています。
英訳② be involved in ...は「…に関わる」、allow は「…を許す」という意味です。
英訳③ 前半は「関わっている日本人がいたら」ということ。
happen は「起きる」という意味です。
その他の言い方：
- A Japanese person would have done something about this kind of error.
- A Japanese person wouldn't have let this kind of error through.
*let ... through「…をパス（合格）させる」
- A Japanese person wouldn't have left this kind of mistake in the menu.
- If there were any Japanese involved in the business, they would have done something about this kind of mistake.
- If a Japanese person were involved in the business, he or she wouldn't have let this kind of mistake slip.
- If a Japanese person were involved in the business, this kind of mistake wouldn't have made it through.
If the management were Japanese, they would not leave this type of problem unresolved.
If Japanese management were in place, they would never leave this type of issue unresolved.
A Japanese manager would not leave this type of problem unresolved.
If の使用で「何々、、、だったら」系の文章を書けますが、回答１と２はその形態です。
回答３は「例えば、日本人マネージャーがいた場合」系の文章ですが、質問のコンテキスト（内容）からして、いちいち説明しなくても、「例えば、、、いた場合」系の文章になっています。ちょっと日本語の発言の仕方とは違うので気を付けてください。
しかしながら、この様な発言を外国人に言うと、「あれ、ちょっと差別的な発言？」と勘違いされやすいので、なるべく避けた方が良いと思います。どの国の経営陣でもピンキリだと思いますので、それよりも "I can't believe management has left this kind of problem unresolved." ->「経営陣がこの様な問題を放っておいたなんて信じられない」的な発言の方が、よりグローバルで勘違いされないと思います。
以上です。
アメリカ合衆国 
カナダ 
