Am I liable if my father passed and there are utilities left as well as a worthless house trailer?

All creditors of your father have a claim for payment that must be satisfied before any assets owned by your father can be transferred to an heir. You do not have any obligation to pay any creditors that your father owed money, such as the utilities. However, if you receive an asset from your father's estate, then the creditors can seek payment from you to the extent of the value of the asset distributed to you. Opening a probate estate and notifying known creditors of the estate will set a time limit for filing claims against your father's assets. All claims must be filed by a creditor within 6 months of publication or mailed notice of the opening of the estate.

No, as his son you are not liable for dad's debts. If you want the trailer, then up to the value of the trailer should be paid to creditors, probably through a small estate affidavit.