Alignment becomes a diagnostic strategy as they get this old. Any adjustments that don't behave normally are what you look for first. Long-term drift from age can disrupt proper peak settings, or a compulsive slug twister could be the problem.
I need to put up a post detailing the dreaded "flush with the rim of the hole" symptom. Any of the skinny tuning slugs that show a "peak" with the top of the slug dead even with the opening are positioned at the end of their functional travel. Turning it clockwise down into the can reduces inductance. Turning it counterclockwise so it begins to protrude above the rim does the same thing. This makes that slug position look as if it's a proper peak.
It isn't. It's the functional end-of-travel position. Means it didn't "travel" far enough to actually reach resonance. Failure of a tiny tubular ceramic cap inside the can is what causes this. When the capacitor takes itself out of the circuit, the coil's resonant frequency jumps upwards. Increasing the coil's inductance brings the frequency back down some. But usually not enough.
You can fix this by replacing the can altogether. Some of them can be "patched" by scabbing a trimmer capacitor onto the solder pads of the right two pins.
Some of them.
But I'm getting ahead of myself, borrowing trouble you may not have.
Just the same, alignment is a diagnostic procedure, even if you don't suspect that a tweaknician was in there ahead of you.
73