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I'm of the opinion that bond and publicEnemy's definitions are both correct.
The purpose of almost everything in a video codec is generally to minimize residual energy.
So that is the purpose of qpel too, but qpel does that by allowing quarter pixel motion to be represented. The idea being that if you represent the motion more accurately, then the error will be minimized.
This does work, and can even result in sharper images.
But there are two problems
1) The motion vectors generally double in size as the enhanced precision means that you need enhanced precision motion vectors! And that can often lead to a loss in overall coding efficiency
2) With DCT based codecs the increased motion estimation accuracy means the DCT noise which varies between different DCT implementations becomes a significant part of the compensation. This results in qpel based artifacts like waterfalls/blurring on image decoding when using different "compliant" dcts.
the DCT problem is not a problem with standards which fully specify the image transform (like h264)
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