From what you have mentioned, it sounds like the SteadyShot is failing to work properly. Try the same test by leaving the camera on a table with it turned on and see if the same problem happens.
In theory, if it is vibrating or moving around too much and you have tried it in good daylight also and the problem is still there then I would recommend having it looked at. There is a repair service which you can book in online.
http://support.sony-europe.com/dime/digistill/cyber/cyber.aspx?site=odw_en_GB&m=DSC-H3
Click the link for repair for more info.
