Both the numbers Beckett's badges on her chest and helmet change from 2202 to the one she uses throughout the series - 41319. This is visible when she is laying on the ground after being shot.
When Beckett is in uniform she wears a Police Officer's shield on her uniform, but Detectives wear their Detective shield when on uniform details.
When Captain Montgomery is giving Beckett his "make your stand" speech, he calls her the best cop he's ever trained. But in Under the Gun (2010), it's mentioned she was trained by Mike Royce. Both are true. Royce trained Beckett fresh out of the Police Academy as a beat cop. Montgomery trained her to be a detective.