The most likely problem for the blurred pictures, aside from camera movement, is the focusing logic in your Nikon. There are so many different settings on some of these newer digital cameras that unless you take a lot of time to learn them and choose which ones work best for your style of photography you may be disappointed with any brand. I use a Nikon D80 DSLR when I have room to bring it and all the peripherals along, it is much bigger and bulkier than the Coolpix. I recently purchased an Olympus TG-610 Tough camera, a small point and shoot, that is most impressive. It is small enough to go anywhere I go, shockproof, waterproof to 15' underwater, shoots great stills and short movie clips. It is nowhere near the camera that my Nikon is but for that class of camera I have been very satisfied with my choice.
One problem most people have with the digital cameras is they are holding the camera at arms length to view and compose the picture using the small screen on the back. Some cameras, my Olympus for example, have no optical viewfinder so you have no choice but to use the screen. If you have a choice though you should use the viewfinder, you can hold the camera much more steady than you ever could with your arms extended, hence more clear pics than not.