Desktop icons cannot be dragged to grid positions.

Doing this aligns all of the icons on the desktop, and then the "holes" become usable. Some icons move a tiny amount. So after the "Clean Up" I can drag the icon to where I want. This more-or-less solves the problem, in that I can put the icons where I want, but it does not explain why the icons became misaligned in the first place, and does not explain why the icons do not just snap to the grid when I release the mouse button. I have always had the grid turned on so they should always snap to the grid. I have not changed the grid spacing. So why do some icons become misaligned? Also, this does not explain why I cannot drag the icons to empty grid positions just because nearby icons are a few pixels off. This used to work; somewhere in recent operating system versions the Finder lost the capability to simply snap icons to the grid when I drag them there. Still an annoying bug but at least there is a workaround. It's annoying because the misaligned icons are not visibly off the grid, so if I drag an icon, and then it jumps across the screen, I have to right-click, select "Clean Up", then drag the icon where I wanted it. Before the introduction of this bug, it was just one operation: click-and-drag, and the icon would snap to the grid position. Now it sometimes is 3 operations: (1) click-and-drag, and the icon jumps across the screen, (2) right-click-and-drag to select "Clean Up", and (3) click-and-drag again. Without solving these bugs, the user interface becomes annoying to use. In summary, now there are 2 bugs: (1) icons mysteriously become misaligned by tiny amounts, and (2) icons do not snap to the grid if nearby icons are very slightly misaligned. Both of these need to be fixed to make the user interface less annoying and to restore this functionality to what it used to be when Macs "just worked".

Yes, I know how to use all of the features described in the link. I have been using Macs for 36 years. The problem is that some of the features do not work in recent versions of MacOS. In short, when you release the mouse button, instead of snapping to the empty grid position nearest the mouse pointer (as they always did for many, many years), the icons jump across the screen to a seemingly random position, often very far away from the mouse pointer. So those grid positions stay empty. The only way to get an icon there is to hold down the control key, but that defeats the purpose of the grid and the icons are not exactly aligned, leading the aforementioned messy desktop. I have not found any pattern to why the Finder prefers that some seemingly random grid positions stay empty. (This happens even when all the icons nearby have short names, so it is not a problem with names overlapping.)

Rebooting into safe mode is pointless and is not relevant to this kind of problem. This problem has been there since I first turned on the brand-new computer, with only Apple software installed. Apple just needs to fix the Finder and stop giving irrelevant "fixes" just to keep me busy until I get tired of complaining. I have been in the software business for more than 40 years, and so I never get tired of pointing out bugs. They can probably find the fix by looking at the code for the Mac OS 9 Finder, which never had any such problem. Also I don't remember this happening with the early versions of Mac OS X. My PowerMac, running Mac OS 10.4, has a slight problem with dragging icons to grid positions, but it is merely an error in the icon's centering/origin. They forgot to account for the icon's origin, which apparently is not in the exact center of the icon. Dragging icons a little to the right and below the grid position always works in Mac OS 10.4. The icon then snaps to the correct grid position, a little above and to the left of where you dragged it to. Possibly they could look at the Mac OS 10.4 Finder code and just fix the small offset problem. Even if they are too dumb to fix that minor problem, it still would be better than what the newer Finder versions do.