I dont what much i can tell about this issue
Let's try to find a pattern with it. For example, it looks as if you are concerned with the "Notification area" icons. Try disabling problem ones from appearing in there (for a test). Right now I would guess that you have Always show all icons in the notification area set. If you undo that option then you can turn off problem icons from appearing in there. It looks to me that different sized icons may be allowed in there. FWIW in my case I have two in there which don't have icons in there at all, just blue boxes where there would be icons, Task Manager(!) and Windows Live Mail. I can try enabling those to see if it helps me see your problem symptom.
Also, you mentioned that you think having had a Fullscreen app open first is a necessary condition for the problem to occur, so my first guess was that display resolution might have been changed by doing that. I think that some apps have such a requirement and that that capability is possible for them. So, for that reason I would suggest using right-click Desktop, Graphics Options, Resolution, etc. to change your problem display's resolution. This tack would also raise the question of whether the problem symptom is evident on another display which might not have been involved with the Fullscreen app. And if you do have another display perhaps you could try putting your Fullscreen app only on it because it looks as if the Notification area can only appear on the primary display's Taskbar. Then that could be a way of avoiding the problem symptom.
BTW I think it may help if you said what you had to do to make all icons appear without the dropdown arrow for the Notification area. OIC. That's when you would turn on the above option. So you would have all icons in there checked including problem ones as well? Then as another change which might be another potential workaround, please see if moving your Taskbar to a side location does anything useful. E.g. I would suspect that all icons might have to be re-rendered for that new format. Even better would be to change the display's orientation, e.g. switch to Portrait from Landscape, since that would almost certainly involve a different re-rendering of all icons due to the display's aspect ratio.
HTH
Robert