Intel "Core-2" processor (refurbished), Dell box, 2GiB RAM. I had all the everyday applications placed on the bottom 'panel.' Then I installed several new packages using Aptitude. Afterward. about half of the icons on the panel had disappeared (or become invisible). The launchers are still there, and work; only the display is wrong.
I had the same issue while I was on Kubuntu. It seems to be a bug with KDE and I have not been able to solve it. Interestingly enough the issue seems to be on Kubuntu but not on openSUSE with KDE and Plasma 5.
Still I recommend you visit Ask Ubuntu or the Kubuntu Forums. It might also be worth, checking back with KDE itself.
Alternatively you can try adding the Kubuntu Backports. This will download some updates for both Plasma and KDE, which might actually fix your issue.
If you have the problem described in this post on askubuntu.com:
then I managed to get back most of the icons by setting again the icon theme as suggested in one of the comments [System Settings -> Icons]. Before installation I had some non-standard theme chosen and it got removed during the upgrade.