It works well for me as long as it is mounted correctly. With my monopod I can hear some vibrations when I move around. I definitely would not be able to handhold it. Hence the search for a good shock mount.
I googled this topic not long ago and found pictures of it mounted a generic looking shock mount. I believe B+H has a video on their website showing it used this way, but when I went there they couldn't help. I wasn't persistent because I was contemplating returning my H1, and I did end up returning it for a couple of reasons, including that the one I had went through batteries like crazy (known defect that affected some of them), and I realized that I do not want a stereo mic. And mostly, I did not want to have to sync in post unless I'm doing a big production with multiple (XLR) mics which the H1 cannot handle. I find that as long as I disable the AGC in my camera, I get good results with an external mic plugged in to the camera. Also, the tripod mount on the H1 is pretty bad. It's plastic (!!!) and my tripod would not go in properly. I did not force it because I knew I was returning it. But it is very light and very portable. I am sure it would make great recordings in the right hands.