When we use the past simple tense, we are telling a story or listing events in the order they happened. It's like a timeline of what happened. On the other hand, when we use the past perfect tense, we want to emphasize that one event happened before another event, like in case when the second event happened because of the first event.
In the case of the example sentence, if we use the past simple tense and say "mixed up," it means we are telling a story of what happened in order. This is appropriate if we discovered the mistake after it happened.
If we use the past perfect tense and say "had mixed up," it means we want to emphasize that the mixing up of the orders happened before we discovered the mistake. This shows that it was a completed action that happened before another past event.
Both past simple and past perfect tenses are possible, and which one to use depends on what the speaker wants to emphasize. In this case, using "mixed up" is appropriate and clear, so there is no need to change it to "had mixed up" unless we want to emphasize the sequence of events differently.