Thanks all, I sent in some of the suggestions. These are the ones I came up with. No exact fits, but I was trying to fit the (what I believe was the) intent.
Around the 80 minute mark, the two main characters (one is Roddy Piper) go to an awards dinner and the speaker is an alien creature (when revealed by special sunglasses).
The Brain from Planet Arous
The main character is possessed by a giant brain from outer space (it pops out of him now and then). Around 56 minutes and around 1 hour, 4 minutes, he addresses a group of leaders each time.
At 76 minutes, Chocolate Chip Charlie (who is about to go on the air on radio) suddenly turns out to be a zombie full of "The Stuff" (it's like yogurt that takes you over).
Around 78 minutes, the leader of the aliens (as a hologram) addresses all the other aliens (who are disguised as humans).
The Adventures of Buckaroo Banzai
There is a scene in this when Buckaroo is giving a press conference and reveals that some of the audience are aliens. One of the aliens is Vincent Schiavelli (Christopher Lloyd pops in as an alien too - but you do not see his true form). That is around the 34 minute mark.