Go w/what Dave suggests. I say prime anyway, and do 2 coats. Fresh joint compound will really suck up the primer! A 2nd coat is just insurance. If you just re-prime the areas you 'fixed', I guess that would be OK. But to be safe, I'd do the whole wall (unless your fixes are more like small scratches/tears, and not very major.) You want 2 primer/sealer coats ESPECIALLY if the top coat is going to be light in color. If you don't prime, you run a high risk of the 'old paint' bleeding through your new top coat. (That's the purpose of the primer/sealer - To prevent the darker paint underneath from bleeding through to the top coat.)
Buy yourself a sanding block and some medium and fine sandpaper. Plan on multiple coatings and sandings. Remember, you can ALWAYS add more compound, and you can ALWAYS sand it off (if it's too much.) Start with a light coating and don't try for perfection. Let it dry, then lightly sand, and add another coat. Feather out the edges as you go, and repeat the process.
A good test for seeing how well you did is to wait until it's dark, then hold a flashlight parallel to the wall, and shine the light 'across' your work. You'll know what to do when you see 'shadows'. Remember - You can add and remove as much as you like.