Is "litter" correct on waste bins?

A litter bin is a bin in which you can place what would otherwise become litter. As such, your objection that the stuff in it is not litter because it is in the bin is at best pedantic; I'd suggest it is at least mildly absurd to be that pedantic over it.

Litter can also refer to a collection of trash. See definition 4b on m-w.com.

Am I right, wrong, or just absurdly pedantic?

I'm sure there are other possibilities than the three you list, Brian. But there is nothing wrong with "litter bin" as a term for a trash receptacle. The idea is that this is a place where conscientious people put litter (which presumably they gather up). Once inside the bin, however, one ought to call it trash.

Er, I agree. It is a rubbish / trash / waste / garbage bin - it may contain erstwhile litter but its contents are the aforementioned synonyms for unwanted detritus. "Litter" connotes miscellaneous, discarded items laying about and which, once picked up and placed in the bin - become mere rubbish.

The sign on the bin is not an exhortation for how we want people to behave, but a label for what the receptacle CONTAINS.