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Yes, sadly one would have to work very hard at taking a worse photo than this example one - out of focus, colour all wrong, etc, etc - to say nothing of those pesky 'yellow fat blobs' all over the place and I suspect you'll fully understand why I literally groaned when loading them into computer and first viewing them - gentle sigh. Most of them taken that morning, I literally dumped immediately if I had a similar one at least a bit better, but although a lousy picture and taken at 6am before coffee, it makes all of us look 'very odd' indeed in so, so many ways, this was the only one of this scene with our grandsons - drat, drat.
Don't worry about it! I've taken a billion (or more) bad photos! TBH I still take them! I'll snap a shot and then look at it and go "What in the hey was I thinking!". Then again, I've snapped some photos knowing that they'd turn out horrid....and they've been great! It's all in getting practice, and snapping tons of photos! Digital knows no bounds! Unlike film, you don't have to pay to look at your photos! Just plop them on your computer and save the ones you like and dump the ones you don't! To easy! Just be sure to look at the ones you don't like and think for a second on how you could've taken a better shot! (subtle hint! LOL!) As for the color, it's not your fault, it's the camera's. There's settings to adjust for that, but we'll go over them at the end.
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Luckily, not all indoor photos taken are this bad - in fact, most turn out 'okay' (but surely not the same quality as those taken outdoors), but I'm afraid I'm guilty of a couple things. First, although the viewer on the camera is a decent size, because I didn't see any 'yellow fat blobs', I didn't always take a second shot - and for help here, I'm guilty of not keeping 'raw' copies (I know, I know!).
That's good news about the indoor photos. The only reason why most outdoor photos looks better is that there's more ambient light to help to expose the shot, so it's a lower ISO and higher shutter speed and smaller F-stop (which the latter of the 3 makes for a crisper image). This is why I wanted you to adjust your ISO and your force your flash on all the time, so that the grain and off-color of higer ISO's won't be present and the light from the flash will illuminate the photos better. More on that later!
Ok, here's the deal: I think that when this shot was taken, it was taken zoomed in (using the digital zoom), and at a high ISO. No doubt the camera's default settings are "auto" on pretty much everything. Hopefully, changing these settings will make a difference in the quality of the shots.
Here's some things to keep in mind when using your camera and taking photos:
Keep off the digital zoom-->it's evil.
Hold camera steady
before,
during and
for at least 1 second after the shot is taken. This will keep from getting blurred photos.
Don't block the flash with fingers...keep fingers off to side. No light means bad picture!
Let the camera focus first (lightly press and hold the shutter button to auto focus). This will allow the camera to auto focus and correctly "judge" how far away your subject is to allow for appropriate exposure settings.
Never use an ISO over 400 unless you really need it (like in a church at a wedding during the ceremony when there's no flash photography allowed). High ISO = grainy photos and off color photos. Same for film. It's just the nature of the beast.
When in doubt, take a half billion photos. Then take a few more just to be safe. Then, take another one. Then, one more just to be safe. After that last one, take another one to be safer. Then another one to be saferer, and another to be safererer...see where I'm going with this?

It doesn't cost you a penny to take 2 shots of something, and most people won't argue having their photo taken twice.
Here's some things that I'd do if I had your camera (yes, I've done it to my own camera):
Turn your flash on for every shot. It won't hurt anything, unless you're shooting from less than 4 or 6 feet away (it'll wash out skin and light colors). If your backgrounds are coming out dark, use the "Slow Sync" mode.....this will capture the picture towards the end of the flash, allowing the light from the flash to illuminate the background more before actually taking the picture.
Turn of the auto white balance. This may or may not nip you in the butt. Always using a flash
should help to correct the color on the majority of your photos. If not, then leave the flash on and turn the white balance to auto.
If there's an "Image sharpening" feature, turn it to either low or off. Try low first, so your images still look somewhat sharp. This feature will sharpen the image when it captures it. It may over sharpen an image causing jaggedness around outlines and high contrast areas. Not having it on my cause your image to look "soft" or "almost out of focus".
Lets recap what we've learned about digital zoom-->it's evil. Don't use it. Just my humble opinion, but I don't like them, as they just take what's already there and make it bigger. You can't take ugly and make it pretty. You can however take pretty and make it ugly. Digital zoom = evil.
Don't use exposure compensation. It's neutral, leaning towards joining digital zoom as evil.
Don't use a color mode unless you really want to. If you do, take a regular shot, then take one in the color mode you want (black & white, sepia, natural or rich. If you can't turn it "off", then just use natural.
Don't go crazy with the different modes. Their over rated IMHO. Simply put it to "P" (Program), turn your flash on, press the button. Yes, it's really that simple. Ok, so it's not that simple!

But really, put it in "P" and turn your flash on either to "forced on" or "slow sync". Other modes will determine if a flash is really needed...don't let your camera decide!
Other tips:
Don't go crazy using your LCD display in the back. That's the biggest thing that will suck the life out of your battery. Be sure to keep your battery charged. You can also buy an adapter so that you can plug it into a wall or car charger to charge it (I believe yours charges via USB on a computer, but it might've come with adapters already!).
Use the wrist strap. Better to have it hanging on your wrist than bouncing off the floor. Cheaper that way too.
Don't let kids play with your camera...unless they can afford to buy you a new one.
Don't touch the lens. Oh, and make sure it's cleaned using lens cleaning fluid and lens tissue paper. Yes, there is such a thing! LOL!
PLAY WITH EVERYTHING ON YOUR CAMERA!!!!!! But don't break anything. Playing around is the best way to learn the ins and outs of something. It'll also let you learn exactly what each mode and setting will do. However, get to the point where you can take good photos first and know the camera well enough that if you screw up a setting, you can fix it. If not, then drop it on the floor breaking it, then blame a grand child and make the parents pay for it. Hey, you spent enough money on them when they grew up, it's ok to do this. Really.
Red eye reduction is up to you. IMHO, it won't work 99 out of 100 times.
Have fun with the movie mode. You'll find it'll be a great way to save memories. You should also be able to save the videos to your photo bucket account and send links to family and friends. Or, just save them to your computer and transfer them using an IM like Yahoo or AOL (blah, I hate AOL more than I hate digital zoom!).
Soooooo....try these settings and see what you get. You'll have to give it some time to duplicate the problem. Let's hope that it won't do it again!
Hope all this jibberish helps!