There are some mistakes in the sentences mentioned above.
Could you find and fix mistakes, if any?
Usually, no comma is put in front of
if but there appear to be some cases when this rule is overwritten.
On the other hand,
if any is quite an elliptical phrase, there need to be put, for example, a subject into it.
Find the mistakes if there's any. (NB: this is an imperative sentence)
Concerning the, I don't think it should be used because it is a definite article but the mistakes are unknown to the reader (co-worker) if they haven't read the text yet. Using any is a good quantifier to stand before mistakes. But if you stick to your plan (of using the), here's the following sentence I advise you to use:
Could you please find the mistakes and fix them (if there's any)?
Mistakes is in plural, so the word that refers to it has to be them.