Well first off, welcome to AVS and more specifically, to the DIY Screen Forum.
Yes...the use of Spackle was your undoing. Spackle may me OK when you want to fill in a nail hole, and then re-paint / touch up a spot o9 a wall. Usually, it won;t be too noticeable, if at all. But when your trying to accomplish getting a smooth, virtually perfectly even surface on which to project a bright image....it becomes the worst possible choice to use.
Spackle is a very fast drying compound that has a very large amount of Silica in it's composition. (ie: sand) Just, as Sand is used to fill holes and level ground in a yard, so also is it used as the "filler" in cement....of which Spackle is...essentially a quick drying, low density cement..
As such, Spackle s consistency and texture is more porous than Drywall Compound, and a order of magnitude more coarse than the texture of paint. It is intended to be used where the use of Drywall tape isn't practical. Very small holes whose presence once filled and painted over would be hard to detect.
When Drywall; compound is put on top of a pre finished surface, it's leading edges must be feathered out so as to virtually disappear, creating a gradual transition, not an abrupt, defined edge. Spackle isn't suited for such fine sanding, nor can it be diluted (thinned) like Drywall compound. As such, on the directions it will tell you of it;s limitations...how big the size hole / area it can cover is.
Another serious oversight is that many people do not re-prime a Spackle'd area. All of the above leads to whatever paint being used as absorbing at a different rate into Spackle, and highlighting the difference between the Spackle and the surrounding areas, usually making the edge stand out despite that edge feeling smooth to the touch.
To correct this atrocity, you will have to apply Drywall compound over those spackle'd areas and to a point where the leading edge of the Drywall Compound is several inches out past the edges of the Spackle 's edges. Then you must lightly sand the edges down until you start to see the Drywall compound thin out and the underlying wall surface start to show through, kinda "hazily". Only sand the center of the recovered area lightly, so that it is flattened and smooth.
Then re-prime the ENTIRE Wall. Better still, after you have blended the offending areas , re-coat the entire screen area with a thin Skim Coat of Drywall Compound onto the entire surface of the screen area, then lightly sand it smooth. "THEN" re-prime the screen area with two, carefully applied coats of primer. Not too thick, so as to not allow excessive absorption into the more porous Drywall compound areas, but rather to "Seal" those areas so the paiont to be applied lies on the surface and dries smooth and evenly.
This will serve to even out the texture differences between pre-finished areas and the repaired areas, and do so much more evenly than simply re priming the repaired spots before re-painting can / will alone. What would be considered redundant if the Wall is just a "Wall" to be looked at under normal light becomes mandatory when you need a perfectly smooth, evenly textured surface.
Look for what is called "Lightweight Drywall Compound" Use a "Large - Fine Grit" Sanding sponge to feather out those "mud'ded" edges.
And now....why don't you relate as to what "the proper screen paint" is and a little bit more about your Projector system and viewing situation. Just might be you need more advice on a broader range of subjects than just re salvaging your wall.