It would be wise to rectify it before transfer of title so your starting off clean and hopefully won't have any issues when you go to sell down the road. 

It seems there are plenty of ways to be penny-wise and pound-foolish. 

If you are making modifications to the heating and air conditioning space of the property it is usually wise to pull a permit.

If you can stomach the negative and any repairs for the next 5 years then long term wise it'd be worth it.

Gas or electric would be a much better option, safety wise, from a house fire standpoint, CO danger, or danger to children or pets from the open flames. 

Where do you want to be numbers wise, and how do you want the property to look one year from now.

I know that anything in California price-wise is far above many parts of the country. 

@Pankaj Malik Good advice from @James Wise, @Nathan Gesner and @Theresa Harris!

Quote from @Sean Barnebey: This is an interesting opportunity, and it sounds like you’re approaching it wisely by considering the numbers carefully.

If the applicant comes from the pool of people that I or my tenants know, I use real estate as a way to give back as many of my tenants will not qualify credit wise or may even have a criminal background or would struggle for another reason if I were to just stick to the "background/credit check" criteria.