It seems to me this Radio-Phono is truly not a vintage unit. If I am correct it is a later production piece from whatever became of it’s parent company Dominion Electrohome. But that’s OK. As for the tuner slipping, I can’t say, as I do not have enough information on your unit to know the tuner works on your radio. Could be a direct drive, or string controled drive, etc.
Why not check out the phono first. That would confirm for you if indeed the audio side of things are working properly. Although if you are hearing static, that is on the positive side of things. As for the turntable, what happens when you try to spin it. Sometimes when a turntable does not spin, it is becaused it is seized up, from hardened grease. It possibly needs a cleaning and lubrication job. We are like your Doctor, you have not really given us any information as to what this unit is doing, in order to help you diagnose it. Some pictures of the unit it self externly and internally may help us understand what you have there. More information is needed.