- Tom had left about half an hour before Jane arrived.
Is there anything wrong in this sentence, please?
No, but the simple past 'Tom left' is also acceptable.
IMO, it should be
- Tom had left for about half an hour before Jane arrived.
Is it wrong?
It's not very natural. If you want to use 'for', then 'Tom had been gone for half an hour when Jane arrived' is more natural.