Are faceplates for different shimano brifters compatible? I got a used brifter and the faceplate fell off. I am pretty sure it was a 105. It works well enough but it looks shitty.

Does anyone know if I can just order whichever shimano brifter faceplate, and it will fit? If that was the case, I might just get one to match my other brifter (a tiagra, I think).
Short answer: 

No they are not. Each model, and usually each year requires a specific face plate.