I personally find that headphones are generally not the way to go for mixing, let alone mastering, and issues that come to my mind right away are fine-tuning the low end, mixing kick and bass, balancing them out well, balancing the different parts of the frequency spectrum or creating artificial rooms and refining a stereo image.
(That said, I have to mention that there are wizzards like Andrews Scheps, who are famous for mixing hit records on head phones)
Let me tell you what some known issues with headphones are:
1. Two sounds sources, right next to your ear...
...under headphones you will hear your left speaker in your left ear and your right speaker in your right ear. All good? Well let me tell you that is not "natural" or rather is not how any living thing has perceived sound over the last millions of years. With speakers, you will hear both your left and right speakers in both your left and right ear, but in different volume and differently timed/delayed. This is called crossfeed, the left side feeds into your right side and vice versa. That is our natural way of hearing things. If you go outside, no sound ever is going to be heard from one ear only, unless it's extremely close to your ear...where does that ever happen ?
...also, in general, under headphones, ear fatigue (or call it loss of sensitivity) tends to set in earlier and we start to compensate the volume level over time which lead to more ear fatigue. This can affect your perception of loudness, transients and frequency response. It becomes harder and harder to tweak a mix or a single sound correctly but at the time the issue is not obvious to us while we are busy doing it.
...more obviously, the pressure of headphones on your ears or your head can cause a feeling of unease or even pain after a while
2. Too Small speakers in headphones...
...that feeling in the guts, that you won't get from those small inch headphones speakers. First of all, you are missing the sensation of feeling the low end response but also, you won't even hear a lot of it through the small inch drivers.
Get a sub pac you say ? It might be able to help you but in my opinion they're nice toys and that's that about'em. For me, they don't mimic the felt low end sound of a room very well.
Personal Experience
Sometimes I get feedback from a client about a song...
...that I have mastered, feedback that I just can't understand...and I'm trying hard to understand, I always try to put myself in my clients perspective. But then very often it comes to light that they haven't used speakers at all but headphones instead or have used mainly headphones for the evaluation of the master, thinking they could hear things in greater detail. And they might hear a small detail that bothers them, but when they come back with feedback, most commonly it's something along the line of "hey we think this is missing" or "...this is too much" when I can't share that opinion AT ALL. And then you know, it is up to the mastering engineer to find out what's going on and communicate with the client in order educate them or simply find a solution...
Each time I was forced to produce and mix...
...under my Beyerdynamic DT880 pro and Sennheiser 280 Pro, I was bummed out by the result when I was able to switch back to Studio Monitors and I have to say, sometimes it felt I have wasted time. Granted, you might have extreme high end headphones or algorithms that do a even better job, but the way you perceive sound from headphones is not a very natural one for us, it's not how we are used to perceiving sound.
It could all be a technology issue though...
...I know there are tools to help emulate crossfeed in headphones and there are headphones built for a more natural stereo perception. I can't say anything about that, I have never tried those tools or headphones. But that's not to say that at some point somebody comes up (or already came up) with a headphone or an algorithm to give a headphones a natural response and make it have a room ambience. But who has that stuff laying around?