One reason the TV picture is poor on the first roundie may be because the CRT has a bad cataract. If removing the cataract doesn't improve the picture, I'd look for weak or dead tubes or chassis problems in the video and/or signal circuits. The second set's tube has a huge cataract as well.
As to the record changer speed problem in the first set, the fix may be as simple as replacing an idler wheel or the turntable drive belt, if that changer has one. In any event, I'd give the changer a good cleaning; chances are it has been collecting dust, dirt and who knows what else over the years, as most non-technical owners of these consoles, as a rule, do not pay much if any attention to the innards of the sets as long as they work; when they start giving trouble or quit altogether, they think the set is beyond repair, so it gets hauled into the attic or garage and is forgotten--until the owner gets an idea to put it on eBay or CL. The set is then replaced with a modern flat panel TV, which may or may not last longer than a year.
And so it goes. Unfortunate, but so often true, especially nowadays.