When we are first introduced to Sergeant McManus, he appears to be somewhat of a bumbling fool who isn't allowed to speak for himself and who is constantly contradicted by his commanding officer.
Sergeant McManus is scolded by Lieutenant Villiers when he accepts the offer of tea from Dr. Hirsch. McManus then proceeds to knock over medical supplies in the Doctor's office and clumsily attempts to put them back into order while both Dr. Hirsch and Lieutenant Villiers look at him like he is a bumbling idiot.
During the questioning of David, Sergeant McManus is open to listening and believing David's story while Lieutenant Villiers is quick to dismiss the story and dismisses Sergeant McManus's opinion on the matter as well.
The next time we see Sergeant McManus, he is much more serious and dressed more seriously. This is after the attacks the night before. This time, when McManus speaks, Doctor Hirsch takes him seriously and is starting to believe this story and starting to have more of an open mind like Sergeant McManus had in the beginning:
SGT. McMANUS: Before nightfall.
DR. HIRSCH: Precisely.
The last time that we see Sergeant McManus, he is dressed even more conservatively with a vest and overcoat on. He and Lieutenant Villiers are outside of the cinema where the werewolf is trying to get out. The werewolf breaks the door down and goes immediately for Lieutenant Villiers, killing him while passing by Sergeant McManus completely.
It's also important to mention that John Landis was actually in the process of writing a sequel and Sergeant McManus was written in as a reliable source to the happenings of the attacks and the aftermath:
She tracks down Dr Hirsch, who tells her that Alex (Jenny Agutter) now
lives in Paris because she was so traumatized by what happened ...
It's then when she speaks to Sgt McManus, the cop from the first movie
who didn't die, that she finds out that Jenny is still in London.
The way that Sergeant McManus is dressed does have some significance in the film. His attire evolves with him as a police officer and his character being taken seriously.
So, Sergeant McManus was introduced to us as a bumbling fool, but leaves us as a credible and well respected police officer.