Why Won't the Patch Tool Work Near the Edge?
The Patch tool in Photoshop is extremely useful for cleaning up dust spots and other minor distractions. It can do an amazing job of blending in your edits with the surrounding image area. Things don't go so well though when the area needing to be patched is near the edge and there is no surrounding image on one side.
The Patch tool examines the color, lighting and texture from where you tell it to and pastes it in to the area needing patched. In order to work its magic, it also examines the area around where you are patching as it attempts to seamlessly blend source and target. All is well if there's enough surrounding area. Using the Patch tool is somewhat like selecting with the Lasso tool. First, make sure the Patch tool is set to patch Source rather than Destination. Then select around the area requiring work. You want to surround the entire area, out into the good parts of the image not needing to be patched. The tool will blend inside and along the selection edge so if you cut things too close you risk cloning the imperfection rather than getting rid of it.
But when the imperfection is right along the edge of the frame, you can't select around it — the selection edge is guaranteed to touch to problem area rather than surround it. The algorithm for the Patch tool looks on both sides of the selection boundary in order to minimize the likelihood the edge will show in the result. When only one side of the selection boundary exists, the Patch tool simply assumes that what lies beyond the edge is the same as what it can sample right along the edge. This means if you need to patch edge pixels, you can't avoid the imperfection itself muddying up the results. No matter where you patch from, the very magic that lets the Patch tool do such a great job normally causes it to do a bad job for edge pixels. It's the blending itself that is the problem.
One possible solution is to paint or clone an appropriate color along the edge before you use the Patch tool. Typically it doesn't take much. Often even a few pixels wide will suffice. Once the Patch tool has something to look, just select the patch source as normal, all the way to the edge. If you still end up with a bit of the imperfection showing, use the Patch tool again with a smaller selection as needed to cover what's left of the problem.
The other option worth exploring is to use the Spot Healing brush on the area first, then use the Patch tool. For some reason, the Spot Healing brush doesn't get nearly as confused about the edge of the frame as does the Patch tool. Paint over the entire area to be patched with the Spot Healing brush or else it will pull what's left of the imperfection back into the area you are trying to fix. Once the entire dust spot or what have you is gone, use the Patch tool as normal to improve how your repair blends into its surroundings. When using the Spot Healing brush, I generally concentrate mainly on getting rid of the problem and leave the finesse of blending to the Patch tool since this is its strength.
Maybe a future version of Photoshop will solve this problem by making the Patch tool even smarter, but for now you'll need to spend a bit of extra time to get the results to come out right.