The W7 has a relatively short shutter lag.
Which makes it sound as if the autofocus is having problems being able to lock.
Reviews show that the autofocus works pretty good on that camera.
It is possible that camera movement is causing the autofocus to "hunt".
Try using a tripod or setting the camera on a solid surface.
See if you get better results that way.
I have a Sony DSC W7. Generally I am satisfied with the results; however I have serious problems with pictures taken in low light using the AF Illuminator. I find it very difficult to get the subject (people or a group of people) in focus. The problem is that the result, viewed on the LCD Screen does not give any indication of a problem. It isn't until you view the picture on a computer that you realise that the picture is out of focus. There is terribe shutter delay but I am satisfied that it is not a shake problem as in many photographs the background will be in focus. The problem only seems to occur when the illuminator is in use.
Does anyone have an explanation or experience the same problem with a Sony camera.