When do mass and volume not correspond to the same density for a given temperature?
Well, they always do. I'm not sure what you're getting at.
However, it's important to note that although the density is calculated as
#\mathbf(rho = m/V)#
and both the mass and volume thus always have an effect on the density of anything, it is only as good as your mass and volume measurements at the time.
Specifically, water will constantly be evaporating slowly, so if you measure the mass of a specific volume of water and write it down, and then wait a few minutes with the water out in the open air, then if you measure the mass again on the same scale, you won't get the exact same mass for your second measurement as for your first.
Furthermore, if you then assume that the volume didn't change (which it did), you've accidentally said that the water is less dense than it actually is, because now you're utilizing an older volume for your calculations that was accurate before the few minutes had passed, with a new mass that is actually smaller than it was before the few minutes had passed.
Granted, this is subtle deviations from the true density, but nevertheless, it happens. If you're worried about this, just parafilm or otherwise cover your container of water while you mass it to limit the evaporation changing the mass and volume.