Well there some good news here. There is nothing wrong with your camera. Indeed, I suspect that, like Jen says, your problems relate to setting and experience.
SHOT #1 – Composition, time of day, and interfering shadows
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The big controversy about the G2 relates to its auto-focus. You should SEARCH that issue on this forum. But you are OK. Even though the bike wheel seems to be out of focus, the bird is pretty sharp – so focus is not the issue! So, how might you re-shoot this assuming that the bird stays put! Well I would start by taking a look at Craig’s-
http://www.photography-on-the.net/forum/showthread.php?t=8620
Here the top-down-back lighting creates uniform on the entire bird .. and .. there are no shadows or foreign objects (SEARCH for ELAND’s definition of SLR where R = rubbish) detracting from the image. Next, your shot seems to have been taken earlier in the morning or later in the evening. The light is great, but the shadows from nearby objects have fallen on the duck’s head and in turn, have reduced the color that you were expecting. In contrast, the water surrounding Criag’s shot seems to be a nice. Not too, that red is the complement is green – so the grass does not offer much color support. Finally. here is a link to a macro shot of my own.. BUT .. you have yo scroll down the original post. It could be sharper (It was hand held in an awkward setting). I am only including these to quiet your G2 fears. (Also, SEARCH for Don Ellis’s G2 shots for further proof of the camera’s abilities. )
http://www.photography-on-the.net/forum/showthread.php?t=3797
Shot # 2 : BACK LIGHTING
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As Jen says this shot is going to be a challenge for any camera. The issue of aperture setting. If you expose for the sky -- the people will be underexposed, and vice-versa. You eye may have adjusted more that the lens! E-comp can help, but I am not expert at that ! However, I am attaching a backlit shot of my own where I was impressed with the play of light created by the sunlit foreground and the shadowed background. You will notice that the Cattails are in shadows, like the "people" in your shot. Your own shot is of course more extreme – almost “black & whiteâ€. However, PS curves, brightness, hue and color balance controls might help to lighten and salvage a bit of the image. I would attempt this for you, however I am running out of “free†online photo storage space.
http://www.photography-on-the.net/forum/showthread.php?t=8828
Keep trying. At this stage it is all a free lunch!