I know some people were salty about Bilbo in the Hobbit movies not wearing the same thing that Ian Holm Bilbo is wearing in the prologue scene of Fellowship, and I hear you. That kind of attention to detail is always wonderful. And I know some people think the explanation that since the voice over is done by Galadriel, she probably just didn't know what he was wearing is a copout.
However...I do enjoy picturing everyone sitting around listening to Galadriel tell the story, and Bilbo starts tugging on Elrond's sleeve and whispering to him like
"Elrond...Elrond...that's not what I was wearing that day."
(being patient with the elderly) "It's okay, Bilbo."
"I didn't even own that waistcoat yet."
(getting exasperated) "It really doesn't matter, it's fine."
"It's not fine. It's wrong. Tell her she got it wrong, Elrond."
(questioning his life choices) "I'm not going to do that, Bilbo."
"BECAUSE SHE'S MY MOTHER-IN-LAW."