Give the following a try. The image is only updated when the button is clicked. Presumably the Dynamic is attempting to continuously update things even though there is no change in the input URL. The following works, mainly because the update of the image is user controlled--but of course it does not explain the problems you are having with the original code... I will think more to see if I can explain the issue (though it is likely covered in the documentation for advanced Dynamic)

ClearAll@interface
interface[] :=
 DynamicModule[{url = "", y = Graphics[{}]},
  Grid[{{
     "Paste your URL below:"}, {
     Row[{Button["Click", y = getFacesFromUrl[url]], Spacer[10],
       InputField[Dynamic@url, String, ImageSize -> 750]}]},
    {
     Dynamic@y}
    },
   FrameStyle -> LightGray, Frame -> True, Alignment -> Left]]

Code retyped...

ClearAll@getFacesFromUrl
getFacesFromUrl[url:Null|""]:=""
getFacesFromUrl[url_String]:=Module[{img,facesBox},
    img=Quiet@Check[Import[url],Return@"Error loading URL"];
    If[Head@img=!=Image,Return@"Not an Image URL"];
    facesBox=FindFaces[img];
    Rasterize@Show[img,Graphics[{EdgeForm[{Red,Thick}],Opacity[0],Rectangle@@@facesBox}],ImageSize-> 700]
]

(*THIS DYNAMIC PART CODE HAS SOME BUG IN MY MATHEMATICA 9
MY NOTEBOOK GET INTO A LOOP WHEN URL IS INSERTED AND ENTER IS PRESSED
THE MSG IS "FORMATTING DYNAMIC CONTENT"*)
ClearAll@interface
interface[]:=DynamicModule[{url=""},
    Grid[{
         {"Paste your URL below:"}
        ,{InputField[Dynamic@url,String,ImageSize->700]}
        ,{Dynamic@getFacesFromUrl[url]}
       }
       ,FrameStyle->LightGray
       ,Frame->True
       ,Alignment->Left
       ]
]
interface[]

Example of Face URL to past into InputField

Notebook Attached

Attachments:

@David Yes!.. I know. I was still polishing it when it crashed.

Nice try with TextRecognize :)

Hi Jim. I was working in a response for your, when my notebook crashed/froze. Here is a print of the code, no time to retype now. It was working fine, but I lost the image url that I was testing.