I noticed I don't have this issue with my Z30 nor do I recall having this issue with my Z10. This isn't really a "how do I fix this" thread or anything, just more of an informational post.
I was out with Sonja last night seeing a Christmas light display and decided to take a few snap shots. These were the results.
http://i.imgur.com/fLYIUj4.jpg
http://i.imgur.com/OMLx6hk.jpg
http://i.imgur.com/foqLVR6.jpg
The last image I can agree isn't necessarily poorly focused as much as the exposure was long and my hands weren't as steady as they needed to be. The first two, at least in my opinion, have a pretty clear focusing issue for some reason. My Z30 doesn't choke on those kinds of photos and I don't recall my Z10 having the same issue, either. In normal lighting, things seem okay.