I do a lot of my work at a small theatre that does not have a wardrobe person for the run, and occasionally, VERY amatur or overloaded costumers. And once we open, the designer is no longer part of the equation.
I've had costumers ask me what sort of format I'd like their information in, ones who have given me genius paperwork, and ones who've handed me hand-scribbled costume plots (which I then typed up in my prefered form). I've had costumers who have NEVER given me plots, and I've had to generate them from what I see onstage. Generally, unless their paperwork is brilliant, I'll take it, thank them, and then type it up in the form I'm used to refering to, and keep both on hand.
And during runs, I will definitely do repairs. At my usual theatre, it's the option of myself (an experienced sewer and historical costumer) making a good repair during half hour, or the ATD slapping some gaff tape on something, or doing some very clumsy stitching, on Monday, days away. I'll do the repair myself, so I know I don't have to worry about it the rest of the run.
But, like everyone's advice, my experience is very site specific; I wouldn't dream of picking up a needle at a "fully stocked" theatre with a dedicated wardrobe crew, or giving any paperwork advice to a designer who's got their act together (well, perhaps except for my tried and true "special laundry instructions" form!)