Is the application icon completely missing (leaving a blank space where an icon might appear), or is the icon just a generic icon (not the custom icon that you would expect to see)
Have you tried a logout from your user - or simply restarted your Mac?
If that doesn't make a difference, try deleting the file com.apple.finder.plist from your user folder/Library/Preferences folder.
then, restart your finder, or logout, then log back in to your account, or just restart your Mac.
If you Get Info for the app, do you see the icon then? Be sure to also look at the "Preview" section of the Get Info window.
That app that you show is on your Desktop. If you move the app to another folder, does the icon appear in that folder? Be sure to change the folder view to List view, then back to Icon view to watch for any changes.
Does the icon ever appear?
Be sure to try a restart (did you do that already?)
Try the same in a different user account. Create a new account just for this purpose.
That will help determine if your icon issue is only within that one user, or is system-wide.
Did you ever get the pixellated icons in PSE fixed? If not, perhaps that issue is related to what you have now... ?
I also see that you have a custom icon for your HD...
Did you use a simple copy-n-paste for that icon, or are you using any software that gives you a variety of sets of icons, to customize your desktop and user appearance? I don't know of any that work well on newer versions of OS X.
That's another reason to be sure to test with a different user account. Substantial appearance mods would likely be gone, and your system would then show appearance defaults.
Can you finally tell me that you tried restarting your Mac? That may be all you need to do!
Did you check that the problem exists (or not) with a different user?
My suggestion would be to log out, then log in to a different user, then download an app that you can't get to show the icon. You could try the same app that you mentioned here.
This fixed the existing app download but not newly downloaded app. The app is "photobatcher" I tried downloading it from Macupdate.com and Download.com. Viewscan, for instance downloads fine. Try downloading "photobatcher"
Of course, the issue is not a corrupted download, but that your Mac is not displaying the app's icon - and for unknown reasons up to this point. Re-downloading the same app for a system issue, seems kind of pointless to me...
The app still works, correct?
And, did you also restart your Mac, when you saw that some recent downloads were OK now, but not NEW downloads?
I would suggest trying that as a first tip, any time you see odd visual effects on your Mac.
I did try downloading "photo batcher" directly from the apps developer, and it appears fine for me. And, I suppose it also still is good for you when you are logged in to the other user account (?)
Are you using any type of download "helper" app, such as Speed Download, or SpeedTao? If you are, you could try disabling, or uninstalling that helper. Perhaps not completely stable, or not updated for Mountain Lion.
As I said, the problem is not with the download. If that was the problem, then you would not see the icon in your other account.
And, your choice of browser is also not an issue (again, the other user account would show the same problem, too!)
Boot to your Recovery partition (restart while holding command-R) and run Disk Utility. Do a Repair Disk (different from Repair Disk Permissions, which wouldn't help you, anyway). If that Repair Disk passes without any problems, restart. and check your icons.
If that doesn't change anything, you could dip into your user folder/Library again, and try more file cleanup.
So, in your Library: remove this stuff: (I'm done with messing around, if you are )
The Caches folder (just drag the whole thing to the trash)
In the Preferences folder, delete the ByHosts folder
The list of files that I previously posted here would still be good to delete again.
Some of those .plist have associated lockfiles, with much the same file name. Delete those lockfiles, too, if you find any (not all will have associated lock files.)