We're in the US at the moment. In a restaurant (BrE) car park/(AmE) parking lot with the Ginger Nut and her family, I had just pointed out that her 15-year-old daughter had a fair amount of her dinner on her (AmE) tank top/(BrE) vest. GN suggested that her daughter ride with us in order to direct us to our next destinations. Better Half teasingly shouted "We don't want that slutty teenager in our car!"
I don't think he'd finished the sentence before I rushed to inform everyone in earshot: "That means 'slovenly' in British English!" (Though the OED tells us that it's now dialectal.) Nowadays, of course, it can also be a not-nice way of describing someone as promiscuous, and that's the only meaning I've ever experienced in the US. The OED has only added that sense in 2004, with examples going back only to 1970--as opposed to c.1400 for the 'slovenly' sense.
The noun on which this adjective is based, slut, was originally used of "A woman of dirty, slovenly, or untidy habits or appearance" (OED), but the "woman of a low or loose character" sense came hot on its heels. While I've not heard women called sluts for being unkempt, I have heard the adjective slutty used to convey that meaning within BH's London-born family. And the next time they come to America, I'll warn them against shouting that other people's children are slutty.