The Face Examiner is a machine that Edd built in "The Luck of the Ed" to examine Ed's face. It consists of two large glass panes, some tape, and a very strong microscope. The purpose of the machine was to examine Ed's face for clues, in order to try and find out where he had been that day and thus, where he might have lost Eddy's magazines.
The machine itself was stored in Edd's basement. Strangely enough, he seemed to have had it premade, perhaps anticipating a situation when he would be called upon to use it. It's usage was largely successful, as it turned up some clues, specifically small pieces of sand that were traced back to the sandbox in the playground. However, this lead came up with nothing, and Ed ended up breaking the machine when the Eds forgot to remove the glass panes in their hurry to get to the playground.