If you’re looking for accurate monitoring, you’re looking at the following things:
A- Calibrating the monitor so it interprets the video signal correctly. On a broadcast monitor, you do this via color bars. With DVI, you don’t really need to do this since the connection is digital.
However, you do need to make sure that your NLE is displaying the colors correctly. With FCP (from what I vaguely remember), you can get different colors (in the viewer) between paused and playing.
B- Calibrating the monitor so that it tracks grayscale well (i.e. black and white images don’t have color casts in them), is of the right gamma, and is of the right color temperature. The gain, bias, gamma controls in most (but not all) broadcast monitors do this. Calibration probes by Sony, Ikegami, Minolta automate this process. These controls aren’t going to fix everything… after a while, a CRT’s colors will get too whacked and should be replaced.
C- Color gamut differences. If no color management is in place (which is generally the case with video), then the color gamut is whatever the display’s natural color gamut is (for CRTs, this is determined by the phosphors). The ideal color gamut for HD is the one that corresponds to Rec. 709 primaries. I don’t believe there are any CRTs that do this… which is unfortunate.
There are LCDs which do Rec. 709 (i.e. there’s a menu setting between it and other color gamuts)… but lower-end ones like the Luma series LCDs only hit that color with a huge margin of error. IMO, the Luma series should be avoided for this an other reasons (i.e. even Sony recommends their CRT lines).
D- Image cheats. With computer monitors, I don’t think you have to worry about this.
With consumer CRTs (TVs), they do things like red push, scanning velocity modulation, flesh tone ‘correction’, and maybe some other things.
Broadcast monitors don’t do this stuff.