A couple of weeks ago I also purchased a superzoom camera and it is a lot of fun but I guess you already know that.
When I just had it I of course also at first used the Auto-mode. If only to see what kind of results it produces. And although it performs quite well under very different light conditions I soon moved mostly to P-mode. Mainly because I want to keep the ISO as low as possible to prevent noise. In bright light conditions the Auto-mode uses low ISO too but if you want to be sure you have to use P-mode. It also enables me to use exposure compensation which becomes desirable with light areas in bright sunlight to prevent washing out and preserve detail.
I'm inclined to think that your photo would have benefited from a little underexposure too. Something like 2/3 I'd guess.
In my case the superzoom I use is a Fuji S8000fd. Since I have it most of the time when I walk the dog I take it with me as it often gives opportunities to get to know different aspects of the camera.
This evening when walking the dog I happened to try the macro feature too. So only about 2.5 hours ago I made this one.
1/38 sec. - F 3.50 - ISO 64
Quality - NORMAL
Sharpness - Hard
White Balance - Auto
Macro - On
Focus mode - Auto
Blur warning - Yes
Focus warning - No (Focus OK)
AE warning - No (AE good)
Since it already was the middle of the evening and overcast I didn't worry much about exposure compensation. With the ISO at 64 I got a blur warning. The IS is basically always on. I expect it is active in Macro mode too.
When trying to keep the ISO as low as possible the IS is an indispensable feature.
Have you also moved away from Auto-mode?