Many programs (usually security based ones) password protect their files for legitimate reasons such as AdAware and Spybot Search & Destroy, there are others (and avast doesn't know the password or have any way of using it even if it did know it). Without examples of the files and locations it is just guesswork.
When you run scans with the above programs and you delete harmful entries that they detect, a copy is kept (in quarantine/restore/backup) in case you need to reverse what you did. These are usually password protected, you should do some housekeeping and delete old backup/recovery/quarantine entries (older than two weeks or so), this will reduce the numbers of files that can't be scanned.
By examining 1) the reason given by avast! for not being able to scan the files, 2) the location of the files, you can get an idea of what program they relate to. You may need to expand the column headings to see all the text.
Files that can't be scanned are just that, not an indication they are suspicious/infected, just unable to be scanned.
Have you tried a google search for 'icons missing on Desktop' (copied from your post), I did and it returns many hits,
http://www.google.com/search?q=icons+missing+on+Desktop.
