I assume you have the video mode set to High Definition (1280x720).
If the camera LCD gives a fish eye appearance, it makes me wonder how it looks on a flat screen television.
It could be that Sony is playing some optical games to get the picture to fit on the LCD.
Check the appearance on the TV, is it OK?
Wide angle lenses can show some amount of barrel distortion, which gives a bulging appearance.
You could take some still pictures with the camera set for 16:9 aspect ratio and see how they look on the LCD and your computer monitor.
To get rid of barrel distortion, all you need to do is use a little zoom.
I own a Sony Cybershot DSC-W350 camera. Whenever I'm in picture mode, the preview on the screen looks fine. But when I switch to video mode, the preview is fisheye (bulges at the center). Why is this? Is there any way to fix it?