Actually, oscillators like a little noise: one old guy trick from the days men were men and oscillators were built on a single transistor and gains were very finite one trick to make sure an oscillator oscillated was to put a cheap carbon resistor in the signal path. The resistor did nothing but generate some nice thermal noise pulses that were enough to kick start the oscillations.
If your power supply has enough noise riding on it to disturbs the oscillator then it's gonna break something else before the frequency goes off.
As the resonator operates at a small multiple (ummm, FOUR?) of the processor frequency (the major power line noise source) you dang well better optimize your capacitors for that frequency. But that's pretty simple anyway, just bypass anything using Vcc at the part. Ceramic caps are good and cheap.
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