If there's nothing in the picture which provides known, measured reference colors, this is very hard after the fact.

If your image does include reference colors, you can sample them and measure how different they are from the standard. Xrite sells the somewhat-traditional Gretag Macbeth targets, or you can buy more affordable calibration targets produced by Wolf Faust. These targets have a wide range of different colors, because adjusting balance to get reddish-browns more accurate may come at the expense of greenish-blues (for example.)

Even if the image isn't displayed accurately on your monitor, you can use the reference data provided with the color samples to calculate the deviation from ideal for the different colors, as Imaging Resource does in their tests. One would use software like Imatest or DxO Analyzer to do this evaluation. I'm aware of plenty of various other software (including free/open source options) for building device profiles from a reference, but I'm not sure of anything else that gives an analysis of error from ideal.

If you color-calibrate your monitor and use an entirely color-managed workflow, you can be more confidant that the image you see with your eyes represents reality as well.

You may also be interested in evaluating your own ability to judge differences between colors — if you have a high degree of color acuity, you may be more confident in trusting your perceptions (assuming a color-calibrated monitor — or a monitor or print that is the final output), perhaps compared to actually looking at the real scene. There are, of course, serious tests used by eye doctors, but I also recently learned (from here) about a neat online test that you might want to try: the FM 100 Hue Test.