Hi guys,
Mixing on good headphones is fine, and acceptable in certain circumstances. It's not unusual to mix on headphones, and then polish the mix on a set of monitors in a treated room. As discussed headphones come with greater hearing-loss risks (but you need to push it a bit, and for long periods). The biggest reason (actually there are two!) to not mix on headphones though has not yet been mentioned in this thread, and it's the reason that headphones mixes often do sound very different once you get them on hi-fi's etc... That main issue is spacial isolation.
If you wear a set of headphones and pan something hard left it will only ever be heard by the left ear, as the ear is isolated, along with the driver, within the cup of the headphones. Same with the right. This means that every element of the mix that you pan (which is often lots of elements!) is massively isolated and distinct. Even only slight pans will naturally be made more defined.
If you perform this same process when sat in front of a set of monitors, in an open room, the right ear will still hear sounds that are panned hard left (and visa versa), it's just that it's only coming from the left speaker. Your brain can tell where the sound source is, but it radically changes the spacial placement of mix elements when you hear them. Often panned elements become either over powered, or very weak as a result of mixing in headphones and require additional EQ and reverb work (as a minimum) to give them the same clarity in a proper speaker mix. Spacial placement is key to an awesome mix.
The other point to mention is the occlusion effect. This, to put it simply (and I'm missing many of the finer points here), is where the sound in the ear canal bounces back and forth off of the skull and resonates from the bass frequencies being pushed against it by the headphones. Much like a certain element in a room having a resonant frequency and artificially 'boosting' those frequencies in your mix. You can hear this effect by talking out loud, and then putting your hands tight against your ears to form an air seal. While you'll loose top end from what you hear, your voice will become boomier in the low mids as the skull resonates from the voice box moving and these waves bounce around in your ear canal.
This is particularly problematic with great headphones, as they often go much lower and are more efficient in the lows than many monitors (and certainly hi-fi speakers), so not only do you naturally get more lows when mixing in headphones, but those lows are often made to resonate higher due to the occlusion effect. The end result here is that your HUGE bass, seems to vanish when you take the cans off and listen on the stereo.
This is not to say you can't make great mixes on headphones, you just have to be VERY mindful of these points, and get to know the headphones, and mix accordingly/compensate. It's no different to an engineer getting used to the traits of a set of studio monitors and the sound of his room.
Hope that helps a little!
Shep