This only seems to occur when I'm running requests in a quick fashion. In this example it's probably doing about 7-9/second, and the popup doesn't stay long enough to get a good screen shot. The amount of data returning is very small less than 50kb..But regardless, even if the data was 1GB, there shouldn't be a popup status window should there?
As a side note, if I run this while RDP'd into the server hosting the web service i get this second image "perf2.jpg" which I would expect ( I guess ).
That "pop up" is a PowerShell progress bar, and its an inbuilt part of the Web-Request command. You can probably set $ProgressPreference='SilentlyContinue' to suppress that.
The pop-up is rendered by the host application. So, when you're in the console host, it's a character-based pseudo-pop-up-thing. I suspect the first time you were using the ISE or some other "graphical" host, which renders the progress as an actual dialog.