Should I just let it go as it's a very obvious clerical error or should I ask they pay me what amounts to about a months salary?
Can you list what country you're in? In the USA, and possibly other 1st world countries, there are numerous case laws in regard to incorrect pay due to paperwork error.
The general ruling is, unless your boss initially made a mistake and you both agreed with it, then you're going to have to pay back anything that you took out once they find out the error. If you have auto deposit, they do have the right to reverse the charge once they find the error. If your bank account has it withdrawn or transferred, then you'll likely get a notice from your bank and the company.
So my advice is to bring the error up immediately and if you do happen to find a very large bank deposit, do not spend it on anything so they can reverse the charge.