I've got Oscilloscope probes that have the compensation adjustment at the BNC end and some that have it at the probe end. Is there any difference in practice where the adjustment is?
Bonus question, here's a bad probe at 10x (1x works fine), it show open from end to end. Any uses for it or garbage?
In practice, there is no difference in how you adjust the compensation of the probes - regardless of which "end" the adjustment capacitor is on. It's just a difference in the internal construction/design of the probe.
As for the broken probe - look like maybe the internal 9M series resistor may have opened up. You can try to repair it, or "glue" the switch in the 1X position and only use it for those infrequent applications where a 1X probe is appropriate.
Bad probe = BIN
Or paint it pink to remind you not to trust it.
Would you know when it is appropriate to use a 1x probe?
Again BIN
That probe is probably now ac coupled to a few kHz with no clue of what the impedance or bandwidth is. So maybe useful in limited cases, but not for most stuff.
I would guess that although there is no theoretical difference in the position of the compensation trim cap that there is a practical one. With a switchable probe at least, if you are going to put accessible parts in the probe, then it is the least costly to add the trim cap there. I think that this also puts the trim cap in a vulnerable position in regards to disturbance from handling in regards to temperature changes and shock. The safer and more stable place for an adjustment is at the connector to the scope. The latter costs more money. Just my guess.
Well, you can use a standard RG 174 BNC connector if you don't put the compensation network there, so...
Also, temperature drift hardly matters for the compensation with a standard x10 probe.
That probe is probably now ac coupled to a few kHz with no clue of what the impedance or bandwidth is. So maybe useful in limited cases, but not for most stuff.
I would keep it, it's probably just fine to use it as a probe for e.g. a frequency counter.