Weak of mind or (occasionally) body, especially if one is gullible or clumsy
Examples:
And then you look at me gormless, like the salmon’s raw when it was requested medium. And what did you say?
— Gordon Ramsey, Hell’s Kitchen (2005)
Now, If I were you, which arguably I am, I would be asking myself in a gormless sort of voice, “Did that bridge really collapse or is my good friend Clarence just playing an hilarious jape?” The answer, monkey man, is that I don’t even know myself. One way to find out. Please, don’t get us killed.
— Clarence, Penumbra (the video game)
[After Angel stops Spike from biting Cordelia]
Spike: She’s evil, you gormless tit!
Cordelia: Excuse me? Who bit whom?
Angel: Did you call me a tit?
Cordelia: I thought he had a soul.
Spike: I thought she didn’t.
Cordelia: I do.
Spike: So do I.
Cordelia: Well, clearly mine’s better!
— Angel, episode You’re Welcome
Etymology:
The word is actually “gaumless”, gaum meaning “attentiveness”. But the British tendency to add an R into their pronunciation (America can sound like Americer) has altered the spelling.