Flatness vs Frequency parameter in RF zero bias detectors
For example, one of the detectors which I am considering shows a
  flatness vs. Frequency of (+/-)0.5 dB max. What does this mean, and
  how can I make sense of these numbers?


A +/- 0.5 dB flatness means that at one point in the spectrum a detected amplitude could be 1 dB lower than that detected at another point in the spectrum i.e. one signal is 0.5 dB down and another is high by 0.5 dB giving a difference of 1 dB and that 1 dB is an error in measurement between two points in the spectrum.

In terms of real numbers, a 1 dB change in voltage is a change of 12.2%. In terms of power it's a 25.9% change.