Time to start putting things back together. I have a week left to get the house ship shape enough to pass inspection. If you remember, I carved big holes in the drywall in the lounge room ...
The fix for things like this is to add some support and patch the hole with a fresh piece of drywall. If you haven't kept the bit you cut out (or someone put a fist through the wall) you actually have to make the hole bigger and then fix it. I kept the pieces.
Here is the hole with some wood support ... remember, you must ensure that the screw heads are lower than the surface ...
Then put the patch back in, screw it in place and run some gauze tape over the gaps (the Spackle has to stick to something).
The Spackle! The trick here is to get it warm (usually by forcing it from one paddle to the other) and then to touch the wall as little as possible. Try to do it in 3 passes. I've seen professionals do it in 1. Also - don't leave tons of excess thinking that you can sand it smooth ... that way lies madness.
My first pass was designed to force it into the holes. The 2nd smooths it out and the 3rd feathers it at the edges. In the pic below, I was a little aggressive in the smoothing on the right - you can still see the gauze.
Once it is dry, knock off the little beads with your paddle (or a cloth) and apply more ... aiming for more coverage and feathering. I ended up putting on 3 coats.
After sealing the Spackle, rolling with the color and cutting in at the corners, here is the result ...
Here is the result after putting the wood work back (sealer, some Spackle, paint) ...