I've been told that using " waiting forward to hearing from you" to end a letter sounds strange. I probably just started using this two words by mistake... many years ago. Is it really an error?
Which would be the best way to wish a prompt reply?
Yes - the usual phrase would be "[I am] looking forward to hearing from you".
If you want to emphasise that you look for a quick reply, you could say "I hope to hear from you very soon", or "I look forward to hearing from you very soon".