My monitor is pretty cheap and its colours are horribly dependent on the viewing angle, the moon and whatnot. I could edit my pictures on my old CRT, but its contrast and sharpness are quite bad.
On the other hand, I never print my images anyway but only publish them on the web. Thus, the important thing is actually what they look like on other people's (non-photographer's) monitors.
In this case, is there any point in spending money on a better monitor or even a calibration set?
Yes, there is a point. It will let you see your own photos more accurately. Since you do not print them, I assume you look at them on your own monitor.
Even if it is only for others, non-calibrated monitors differ widely but they are improving at least in the mid-range with the advent of LEDs (and eventually OLEDs), so over time people will see your images more accurately. Having a good monitor will let you know better how you images will appear to others too then.
Calibration goes a step further and is highly recommended if you manipulate your images since it will let you see the effect of your changes. Otherwise you can introduce very unnatural looking colors.
If you have to choose one though, I'd go for a better monitor. You can always add calibration later. Finally, if you do not require a huge display size, great color-calibratable monitors are no longer than expensive. I always recommend the NEC P221W even though I don't work for NEC ;) but I spent years evaluating LCD displays professionally. I bought two of those refurbished for $237 each while they go for $450 new. There is also a 24" version, the P241W.
Yes.
Using a calibrated monitor effectively makes your monitor a "control" and the variations found when viewing the images on another display are going to shift it from that control colour and exposure. You want your monitor to display the photo exactly how you want it and the others to only be different due to their limitations.
When you don't use a calibrated, higher quality monitor (such as an old, low contrast CRT), you're not seeing what you should be seeing. You're calibrating your white balance, exposure and contrast based on an skewed image. If your monitor is slightly too bright and slightly too warm, then your images displayed on a calibrated monitor will probably be darker and cooler than you expected.
Yes, you should care, as the colors that are seen by your audience can vary surprisingly dramatically. You should attempt to be as accurate as possible, but sometimes it doesn't even matter, especially if the browser your audience uses isnt color managed. These days, this is less and less an issue, as Firefox, Safari and even Chrome support ICC profiles.
To see some of this variation, I refer you to SmugMug's Chris Macaskill's blog on the subject:
http://blogs.smugmug.com/great-prints/2008/05/29/smugmug-alters-my-colors-updated/
http://blogs.smugmug.com/great-prints/2005/06/25/smugmug-alters-my-colors/
You should note that as a result of these, SmugMug changed its policy and began embedding ICC profiles in its images to aid in proper color reproduction.
Also, if your images are only going to be shown on the web, be sure that your camera is set to sRGB colorspace, not Adobe or Prophoto, and that when saving in your editing tool that you are not saving in a different colorspace, which happens too often.
