Your father's probate estate is responsible for the repairs (assuming that your father owned the property outright and not through an entity, in which case the entity would be responsible).
To the extent you accept rent, you are effectively acting as an agent of your father's estate in anticipation of being appointed to administer his estate. As his likely successor in the intestate estate, you have an interest in making the repairs, if urgent and if this mitigates the long term cost of the repairs and of the liability to the tenant for not making repairs promptly, that you would ultimately end up bearing.
Often, it is possible to get appointed fairly quickly, at least on an emergency or temporary basis pending a formal permanent appointment to administer his estate. Doing so, if you could, would take you out of the shadows of acting in reliance on your future authority to act on behalf of your father's estate that you have not yet been granted.
If you accept rents and make repairs and then someone else ends up being appointed to administer your father's estate (e.g. because a will you didn't know about is discovered and appoints someone else) and if the person ultimately appointed is displeased with the actions you took without formal authority to do so, rather than ratifying those actions, you are in a bit of a pickle and could incur some legal liability to your father's estate that could reduce your inheritance if there are also other heirs.
You also have the option of simply walking away from his estate, not trying to be appointed to administer it, and not trying to claim an inheritance. If you do that, you have no personal liability to your father's tenants at all.
If the situation that your father left behind is a truly troublesome mess and his estate is probably insolvent, it may even make rational sense for you to do that.
You can't be held responsible for inaction in any way other than the depletion of your inheritance that arises naturally from your inaction. If this is the case, however, you should not accept rents from the tenants or have any other involvement in the management of your father's assets.