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I think a 388 in excellent shape should go for no more than about $500, maybe $450 would be better. You want it to be clean, overall. You want to look at the heads and lifters very closely under bright light. A new head has a curved surface, and any wear would be a flat spot. You want the head wear to be minimal and even, not
keystone shaped. You can also see wear on the lifters, which is relative to head wear. Moderate wear on the heads and lifters would be normal, excessive wear could be problematic. You want it to record and play back properly. 2-3dB dropoff between record and play levels would be typical for an older device that's not been calibrated, but this can be adjusted out. On playback you want to watch tracks 1 & 8 for waveriness, which would indicate excessive head wear. You want all the faders to feel firm and smooth and not loose or bent. You want all knobs and faders to be scratch free, but a lot of this can be worked out with use. Toggle switches should be functional and noise free. VU meter lamps should all light. You'd typically want all the colored caps on the knobs and buttons to be present. FF/RW should be brisk and efficient. A properly adjusted servo would present the tension rollers' centers to intersect with an imaginary line that's drawn across the bottoms of the tack and idler rollers. When
servos are properly adjusted the FF/RW functions best. If either of the tension rollers look like they're sitting a little low during play function, you'd probably expect the FF/RW to be inefficient and sluggish. Not a huge concern as this can be adjusted out. You want there to be no flakey or broken connectors on the back, headphone jacks functional and noise free. You could take one mic or signal source into one input, assign it to all busses and record on all 8 tracks simultaneously, then play back and see what it looks like. Hopefully the plexiglass tape cover is clean and scratch free. All the transport buttons should be in good shape and fully functional. The whiteness of the buttons should be light and not dark. Some yellowing is normal, but excessive yellowing might indicate a smoker's environment, which generally is bad on equipment. That covers a lot. I think head wear and overall condition are most important. You don't want excessive head wear or to look at the unit and find it looks like grimey gooey who know's what is all over it. Simple dirt can be cleaned off with some effort. When I've cleaned a unit like this, to remove all the knobs & faders, clean the mixer plate and knobs individually with cleanser would be common and well worth it.