Well, I dont really know if there is much you can do since youre using the rig provided by epic, right? Anyway, there are a few things I can share:
1. The "T-pose" is usually the middle between the extremes to reduce geometry- and UV distortions to a minimum. If you look at the UT2004 T-pose (or even at the one from UT3 which is more extrem) you will notice that the characters arent ment to raise their arm like that at any time (no climbing, grabbing, etc). So any animation which raises the arm will have its difficulties.
2. If the characters have to raise their arm in UT2004, most of them have huge shoulder pads to cover those areas.
3. Also, most of the characters inlcuding yours from the gif are quite lowpoly. Having only a few Polys available on areas with a lot of movement is obviously bad

But... old engine, cant be helped.
4. A proper edge flow will help reducing difficulties to a minimum. Many beginners just extract an arm out of the upper body (like this:
http://digital-sculpture.co.uk/wp-conte ... geflow.jpg or this:
http://4.bp.blogspot.com/-GKFG2TRQht8/T ... dymesh.png ) and that is complete crap. The pectoralis and the delta muscle have to be in one edge flow (like this:
http://blenderartists.org/forum/attachm ... 1354815017 or this:
http://www.creativecrash.com/system/pho ... 1277393552 )
4. The rig itself (bones, joints etc) is very simple in UT2004 and doesnt support much of the extras provided by maya or max. As far as I know it doesnt even support Blend shapes. So yea, like you already said, having only joints and bones available makes life hard.
5. And at last one important thing which I see being done wrong very often. Most of the motion when raising your arm comes from the shoulder (the trapezius) not the delta-muscle. You can try that out by letting your arm hang relaxed and putting your other hand on your shoulder. Then lift your arm slowly straight up (some sort of a flying motion) and you will see that the shoulder will start to raise very very early. I dont know if the animation from your gif is made by epic, but you will see that the shoulder doesnt move up even a bit. All whats moving is just the upper arm and the result is the twisted shit. Besides, the whole arm is completly out of order when its up. Someone really fucked up there.
Art in a frame is like an eagle in a birdcage.