"The goofy teeth seem familiar, but the tiara has me baffled!"—Doctor Bender, The Fairly OddParents.
The opposite of Latex Perfection, and often a special case of Wig, Dress, Accent. A character that the other characters should recognize (or at least recognize as not belonging) dons a disguise. This disguise is so completely transparent that the audience wants to shout "For the love of God, it's him!"
The reason may be that they want the audience to know before the character does (a sort of Reverse Whodunnit), but it seems more likely that it's a matter of the character being a Special Guest, and the director wanting to get his money's worth out of them.
All the same, you often get The Reveal staged in such a way to make it clear that the director really thought you wouldn't have worked it out by now. For the more perceptive viewers, it's a case of The Untwist.
This trope differs from the general case of Wig, Dress, Accent in that a Wig, Dress, Accent disguise is always plausible. Paper-Thin Disguise also includes the element of being staged as if the disguise really is convincing, which is not generally present in Wig, Dress, Accent.
While this is not quite a Discredited Trope, it appears in parody at least as often as it is used seriously. Children's shows still employ this regularly without remorse, and it is a dramatic convention in theatre and opera as the character still needs to be recognizable to the audience from the seats (similar to becoming totally inaudible by walking upstage).
This can sometimes be exaggerated to the point of comedy. For example, you can wear bunny ears and become indistinguishable from a real rabbit, or pretend to be an ancient statue by simply standing still in a specific pose.
Also See Conspicuous Trenchcoat, Not a Zombie, Newspaper-Thin Disguise, Clark Kenting, Mr. Smith, Hugh Mann, Holding Both Sides of the Conversation, Charlie Brown From Outta Town, and Most Definitely Not a Villain. Contrast with Full-Body Disguise.