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Not sure, but I wouldn't touch this deal with a 10 foot pole. Too many ways for it to backfire on you.
A 30 day late is a minor baddy. Once it turns into a 90 day late, it is a major baddy. Even if it is a minor baddy, it will hurt your scores for years. Also note, if your name is on the mortgage, they can come after you in the case of a foreclosure or suit.
I assume your dad thinks if you have a mortgage on your credit report it will make it easier for you to get your own mortgage later. Even if the payments history was perfect, it would probably backfire due to the mortgage payments counting against your DTI. Meaning, your mortgage company will want to see enough income to cover your father's mortgage and your mortgage. And they will not count your dads rental income since it is not going to your bank account.
CD and others are right (for the various reasons cited). This would be a very bad idea.
If your father wants you to be able to have a better credit profile from a mortgage lender's perspective, the best thing he can do is to support you in continuing to learn about how credit scoring works and to take your own steps to improve your profile. This involves paying your CC bills on time and in full each month (along with any other monthly bills you have). If you have never had an installment loan before, that would be a nice thing to have in your credit history -- future mortgage lenders will like seeing that you were able to manage and pay off one. There's some people in the forum here who can explain safe cheap ways to add a $500 installment loan if you have never had an installment loan before.
Above all never EVER be late with even one payment on any account -- or share accounts with anyone who might be.