Didn't find this exact issue with a search, so here we go...

K3S #10299. 

I have been experiencing low output on 12 and 10 meters, so did a TX power calibration run with K3 Utility to see what I could see. 

The 5W calibration failed at 12m:

...

Calibrating at 21.200 MHz

Calibrating at 24.930 MHz

TX Gain calibration failed because transmit power did not reach the expected value

5 watt calibration failed

Elapsed time: 45 seconds

...

Calibrating at 21.200 MHz

Calibrating at 24.930 MHz

Calibrating at 29.000 MHz

Calibrating at 52.000 MHz

50 watt calibration succeeded

Elapsed time: 57 seconds

Run the MW gain cal, if it passes without high numbers on those trouble bands, then the LPA probably has a weak final.
If the MW fails, the BPF needs to be tuned, maybe a tweaker replaced. 
FYI you can run the TX gain cal individually on your favorite freq. Manually set TUN PWR to nor, set to -exactly- 5.0 watts, long press XMIT to do a TUNE for several seconds. Repeat at 50w and for 1.0 MW, set  KXV3 to test mode.
You can check the TXGN menu to watch the numbers before and after.
Keith WE6R Elecraft K3/K4 Tech

Keith, Thanks!

Indeed 1mW cal fails at 24.930 MHz, Calibration power settled at " 0.24 MW;"

BPF alignment procedure suggested by Wes N7WS below, is this still what you would recommend? 

Alignment should begin on 10-meters because that is the primary design band for the BPF.  Elecraft very cleverly exploits the fact that the secondary bands (12, 17, 30 and 60 m) are very narrow and can be tuned with just additional parallel capacitors.  Unfortunately, I am not privy to what the 10 m alignment frequency should be.  I would guess mid-band if the filter is truly symmetrical.  Personally I don't operate high in the band, so I might be inclined to use a lower frequency.

For the moment turn off ALC and in Tune mode set a low level, 1-2 watt, tune C180 and C184 for peak output.  Switch to 12 meters mid-band and adjust C181 and C185 for a peak.  That should do it.  I would observe the smoothness of tuning while making the adjustments.  If anything is jumpy I would suspect a bad capacitor or solder joint. Restore ALC and repeat the TX gain adjustment. 

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73, Paul K6PO

OK, fixed. At least for now. C180 was flaky; I resoldered it and peaked it and C184, and TX cal completed on 5W, 50W, and 1mW. 

I'm not really sure resoldering C180 was the cure, maybe just sweeping it back and forth a few times cleaned it. What is the typical failure mode on those variable caps? Should I just replace it?

Anyway, many thanks to Keith WE6R and Wes N7WS for good guidance on this. Much much appreciated.
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73, Paul K6PO

Most bands are in pairs, (160 & 80 are just two adjustable caps for both bands, 6m has it's own 3-caps).
So on the pairs you tune the higher band first as it affects the lower. If you only work on the lower band, you can probably get away with not tuning the higher.
Tune the pairs in this sequence;
40m then 60m,  20m then 30m, 15m then 17m, 10m then 12m.
We sweep the whole band and watch on a Spectrum Analyzer; In to the antenna, pull mixer and take the signal out there back to the SA.
The narrow bands you can get away with peaking, but wide ones you should use the SA as it is definitely -not- a flat line. 
I have had good luck rocking the yellow caps to clean them up.
The old blue ones should be replaced if flakey, I usually just replace all of them. 
The orange ones don't fail much, so I just replace the bad one. 
The latest K3"S" has surface mount caps that have not seen a failure.
Keith WE6R Elecraft K3/K4 Tech.
Not sure how to post a picture;