wvmarle:
At 10k you don't need to do anything special: that's the recommended limit to input impedance for the analog pins.
With the capacitor you should be able to go to 100k without issues, maybe even higher like towards 1M, but if you get into that kind of values it's time to consider adding a buffer. A cap on the input does slow down reaction so not good for fast changing signals.
I regret insisting: I've made a project involving a pro mini and made many (more than a dozen) tests with different units, either chinese and Sparkfun ("half genuine") ones. Every time I noticed an unstable behaviour with sensors whose impedance is greater than those values, even adding a cap.
As many other characteristics of this microcontroller, this parameter is not well docummented and this behaviour has no apparent reason. I just tell what happens.
Best regards.