I can (Present) correct the mistakes ... if there will (Future) be any OR if there would (Conditional) be any?

The correct complete sentence would be: I can correct the mistakes if there will be any.

The form for the future "Will" expresses a lot more certainty than the conditional "Would", which usually refers to imaginary situations. If the sentence were "I could correct the mistakes", then the conditional form would apply better. Then, the sentence would be an example of the Second Conditional, where an imaginary situation leads to its consequence, and the conditional agrees with a verb in the simple past. Another example of Second Conditional: If I became rich, I would buy a car. In this example, the situation is entirely imagined and the conditional "would" agrees with the past form of the verb "became".

The sentence in question is an example of the First Conditional, where there is a direct consequence (future) for something that happens (present). An example of First Conditional: If it rains tomorrow, I won't go to the park. In this example sentence, not going to the park is a direct consequence of raining.