The sentence is polite and if you were to say it to someone they'd instantly know what you're trying to say. The correct form of that sentence would be "I would appreciate it if you could check my writing and tell me [what] my mistakes [are]" I think it's more natural to say "and point out any mistakes" though. Square brackets are optional, but if you use one you have to use the other alongside it. It's probably more natural to frame it as a question in most contexts though: "Could you please/Please could you check my writing and point out any mistakes?"

Hello! This is a better way of saying it: "I would appreciate "it" you if you "could" check my writing and tell me what the mistakes are." I have added "it" because it specifies what "would be appreciated" and I have added "could" as this is the appropriate modal verb for suggesting the possibility of what is being requested. I hope that helps!

It's almost right. Here's one way of correcting it: "I would appreciate it if you could check my writing and tell me what the mistakes are." And yes, it's a polite request.

Either: "I would appreciate you checking my writing and telling me what the mistakes are." Or: "I would appreciate it if you could/would check my writing and tell me what the mistakes are."