In The Dark Knight , when The Joker plans to kill the Mayor at a public gathering. His attempt to shoot the Mayor is foiled by Gordon. After this we see Joker's face in frustration. This is the only time we see Joker without his make up, but the scars on his face are clearly visible.
Why is it that no one noticed this highly unusual man dressed up in a police uniform at this function?
One of the reasons that no one notices The Joker dressed as a police officer is because there are hundreds of other police officers that are all dressed alike.
The joker does not have his normal green colored hair and blends in quite well with the other police officers. The only distinguishing features are the scars on his face.
Other factors to consider:
The firing squad consisted of The Joker and his men. They would be the only ones close enough to him to be able to recognize his scars.
Nobody has ever seen The Joker without his make-up on. The police would be on the lookout for The Joker based on the only description that they know of him and that is of The Joker with his signature make-up, clothes and green hair color.
The police Department is already shown as being corrupt. The Joker could have easily used corrupt police officers to help divert attention away from him.
Gordon and his men seem to only be concerned with watching the windows in the buildings above the parade route for snipers. You can notice Gordon constantly looking up every time you see him until the firing squad starts firing: