This is on the bonus DVD when D. Nadoolman begins talking. It's the Idol Grab scene, too early in filming to be real sweat. I think some type of oil might have been brushed on. Also, I've noticed this dot on the brim for years. It's in a lot of scenes. Looks like it's from this oil aplication. Oil could have been applied above the ribbon. Look at the little dark triangle on the felt near the corner of the bow, and how it pics up dust in the b&w pic.
They did the location shoots before they did the Elstree stuff so in all fairness to those who think it's JUST sweat, it may be just that. Of course, if this is a new hat then it's safe to say it was completely distressed. Like the Kennedy assassination, we'll never know.
I'm with you on this one 3K. I think there are a few nice tricks they could have used to get the hat looking old and used.
Also, I've noticed this dot on the brim for years. It's in a lot of scenes. Looks like it's from this oil aplication. 
Oil could have been applied above the ribbon. Look at the little dark triangle on the felt near the corner of the bow, and how it pics up dust in the b&w pic. 
