HDR is NOT for moving objects.
And it doesn't work how you think it does either; it's not necessarily ISO-sensitive (although it can be.)
HDR is a compensation for the fact that digital image sensors have less dynamic range than film did. So what the camera does is take successive exposures bracketed around what it measures to be "correct", intentionally overexposing some and underexposing others.
This allows the capture of both highlights that are "blown" at the "correct" exposure and also capture of shadows that are black ("dead") at the correct exposure. The camera then takes those images and replaces the highlights that are blown with the properly-exposed ones along with the shadows from the other exposures, rendering one image with highlights, central tones and shadows.
The problem is that it has to capture multiple frames to do this in succession, and if the subject is moving you get blurred motion -- not because the shutter speed is too low but because the subject(s) moved between successive exposures. There's nothing you can do to prevent that from happening in a HDR exposure.
I create manual HDR exposures all the time with my dSLR; I take a bracketed set of shots that intentionally over and underexpose, and then combine them in post-processing. Same problem applies although my Canon 7d can shoot the bracketed set of shots at 8fps -- if the subject moves during that period I'm screwed.
The Z10's HDR mode is surprisingly good for a cameraphone. The biggest issue that it, like all current phone cameras have, is that by not giving the option for raw capture you're stuck with the loss of information that JPEG compression imposes. In addition cellphone cameras have very poor depth-of-field control because the sensor is so small -- there is nothing that can be done about that as it's a function of the size of the sensor itself (and is the reason that "full frame" cameras can produce superior depth-of-field effects over crop-sensor ones.)
Finally the "burst" mode on the Z10 is simply out-of-this-world for a cellphone. The included image coprocessor is likely responsible for that; I've not found a buffer depth limit on it yet, and that surprised me.