One thing's got nothin' to do with the other.
心猿意马并不好里昂你明白吗?Change ain't good, Leon. You know?

我知道Yeah.

检查一下Check it.

确定这玩意儿没问题Make sure it's the right thing.

我相信你I trust you.

相信别人容易出事One thing's got nothin' to do with the other.

你要记住里昂Remember that.

我会的I will.

what is"one thing and the other refer to" in here?

the dialogue begins with the 45 minutes and 17 seconds in LEON

Question

One thing's got nothin' to do with the other.
心猿意马并不好 里昂 你明白吗?Change ain't good, Leon. You know?

我知道Yeah.

检查一下Check it.

确定这玩意儿没问题Make sure it's the right thing.

我相信你I trust you.

相信别人容易出事One thing's got nothin' to do with the other.

你要记住 里昂Remember that.

我会的I will.

what is"one thing and the other refer to" in here?

the dialogue begins with the 45 minutes and 17 seconds in LEON

Answer

To translate 相信别人容易出事 as One thing's got nothin' to do with the other. is a very 'free' translation.

What he or she means is: even if you trust me, you should still check.

In German there is a saying: Vertrauen ist gut, Kontrolle ist besser. That means: Trust is good, but it is better to check as well.

Answer

one thing= some one`s affair, or some thing!
 other=other one! some one other`s!some other thing!