Spider-Man 3 Clip: The Birth of Venom 

i guess there must be a bit more in the movie because he suddenly goes from a hoody to a t-shirt

Oh nice catch Matt, maybe it was an editing mistake! I can't seem much happening where he takes off his sweatshirt and throws it off before the Venom suit descends upon him.

Actually I think there is more, as I remember seeing a part where Peter is ripping off the suit, and I did not see it in this clip. It would be really hard for me to discribe it though.

ATTENTION! I was looking on Youtube and I found this trailer with mostly Venom. It shows Eddie (Venom) taking off his jacket. It also shows why Spider-Man was attacking Harry in the weapons shelter.
http://www.youtube.com/watch?v=qyKQjZkZZPf­o&a­mp;­NR=­1