I have taken a lot of pictures recently on an overcast day. The pics are good and the colour temperature is setup well but the photos that feature some of the sky don't look as good because the sky is just completely white like an underexposed white background.
Is there anything I can do to make that sky look a bit more interesting?
The only thing you can do with a completely flat sky is Photoshop (or GIMP) in a more interesting one. If there is some texture in the clouds you can boost contrast and lower exposure a little to emphasise the details, but if it's pure white/grey there is simply nothing to work with.
When Photoshopping in a new sky (not as uncommon as you might think), try and choose one that could conceivably give similar lighting to the ground as the 'real' sky - in this case, a blue sky with fluffy white clouds taken on a sunny day probably would not work. You would instead need something fairly cloudy.
If you are unwilling to go to this length, perhaps the only other thing you could try would be to add some kind of graduated colour filter to the image, perhaps a tobacco or warming filter.
It depends on how overexposed it is. If it's really completely white and featureless, then there might not be anything to do, short of ElendilTheTall's suggestion of Photoshoping a new sky altogether.
But, assuming you have the RAW files and a RAW processor, I would first try to bring out some detail in the clouds. At the very least, make them a little darker while keeping detail in the rest of the photo. A quick outline how to do that:
Decrease the exposure of the whole image a bit.
Add some "Clarity" to increase the local contrast in the clouds.
Decrease the exposure of the highlights.
Increase the exposure of the shadows.
As with anything, adjust to your own liking. If the non-sky part of the image is also bright, you may need to use local adjustments to limit the above changes to just the sky.
