The original sentences are mostly clear but can be improved a bit for grammar and flow:
Original: Magpies are very smart. They know the bird they see in the mirror is them, not another bird. Magpies also make funny rattling sounds.
Corrected Version:
Magpies are very smart. They know that the bird they see in the mirror is themselves, not another bird. Magpies also make funny rattling sounds.
Explanation: Adding 'that' after 'know' makes the sentence clearer. Using 'themselves' instead of 'them' is grammatically correct because it refers back to 'magpies.'