So much noise

That grainy speckle that often infects digital photos taken in low light, is normally called noise, (maybe it is called dark noise, heat noise or salt & pepper noise). It happens when exposures are longer and/or the ISO setting are higher because adjacent receptors on the sensor are charged up longer or more to become more sensitive. That allows heat or current leaks onto the adjacent receptor which interprets it as more light. There are a whole range of methods and algorithms to detect and try to remove this noise. Many such methods are now being built into cameras. They seek to work out what is an artifact of the noise versus real detail in the photo. Some methods look at variation in brightness or luminance (Lumina) other look are variation in hue (chroma), the little specs usually appear variable colours (see below). I find with my camera the chroma noise reduction leaves a better quality filtered image and removes the “digital camera grain” best. However all noise reduction will lead to a slight loss of detail and quality in the final results, typically a smoothing effect.

BEFORE

AFTER

From my perspective noise reduction is the one remaining obvious thing missing in picasa’s simple photo editing tool kit. Unfortunately the best NR (that's Noise Reduction) Software is still relatively expensive and mainly available only as plug in for Photoshop & Lightroom. Don’t despair, a free download trail of noiseware (either as a plug in or standalone) will give you decent results before you need to fork out big bucks. The above example was created with the Noiseware Community Standalone version (free and no trial period). Good Noise filters are available for Gimp.
There is a lot of hype written on the net about NR tools and most are actually much of a muchness, but without testing it is difficult to appreciate subtle differences. Pro Photography Show gives a decent review of leading NR software by way of a number of downloadable high resolution before & after images so you can see for yourself.

It is wise to have at least one such NR filter method available to help you recover an occasional dark photo or even a whole series from your party when the photographer may not have be concentrating.