It's called "spiking guns." Have your facts, and present them. Either he shuts up about the broken stuff, providing you with "last-nerve" relief; or he takes you up on your offer, which provides you with stuff that works and rent relief; or he argues about your prices, at which point you say, "As my landlord, you are responsible for maintenance on this rental property. If you can fix these things more economically, please do."
He's enjoying a revenue stream that requires next to no effort on his part ... make him work for it a little. You have to work for your rent ... a lot!
I meant “filthy” as in it looks filthy. My word, not his. He’s not really seen it much, and he didn’t say anything this time, but he had to have noticed.