She could be listening to a radio.
They could make them small enough to fit under that coat in 1920, especially if it was a simple crystal radio... and they could certainly make a set of earphones small enough to be handheld. In fact, if it's a crystal radio, it'd want to have a handheld speaker in order to be be audible over the crowd.
I'd guess it's probably some gadgeteer mucking around with an early radio Walkman. "Oh it's too bulky and heavy to carry around.... it'll never catch on"
Or just a nutbar who brought the earpiece of an old telephone out, and thought it was possible to communicate wirelessly with it.
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--m(^0^)m-- Wot, no sig?
Can you hear me now?
If they are talking on a cell phone, then they have one hell of a roaming plan. I want to switch to their service provider.
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"Anyone can be a winner if their definition of victory is flexible enough." - The DM of the Rings XXXV
Well, yes, that's one hole in his logic. But it doesn't eliminate some other variety of hand-held transceiver. It's just that the most common example these days is the cell phone -- twenty years ago and someone might have said "communicator" or "walkie-talkie".
Dartz -- while crystal sets could be -- and generally were -- small enough to be hand-held, the "cat's whisker" detector/diode is a rather delicate affair (being, as the name suggests, a hair-thin wire brushing a crystal of galena or other semiconductor mineral) and wouldn't stand up to being toted around. Plus, they didn't have speakers that could be heard over a crowd, even if you held them to your ear like a transistor radio -- they used ear phones because they generated such a weak sound (being powered by the radio waves they picked up, not by an internal power source). If it were a crystal radio, as unlikely as that might be, she'd have a wire from her ear to an object in her hand, pocket or purse instead. (My dad was a Depression-era child and knew how to build one with a cardboard oatmeal canister and box of scraps -- cave optional -- and showed me how to do it when I was a kid; I know from experience that, ruggedness of cardboard aside, they don't hold up to handling too well.)
And it can't be any other kind of period portable radio, because they didn't exist -- powered radio at the time needed vacuum tubes and a wall socket, and tended to be in big boxes. The first man-portable radios were those backpack units you can see in old war movies, where one guy wears the radio while another cranks up the magneto for power before transmitting. And this film predates that technology.
Anyway, the best way to figure this out is to figure out all the other things she could be doing that would look like that, as some of the folks in the comments on that page have. However, some of those suggestions just don't pass the reality check -- anything that involves her shading her eyes would have her holding the whatever-it-is in a different position, as we can clearly see that it's not shading her eyes at all -- the shadows don't line up with the direction of the light. (If anything's shading them, it's the brim of her hat.)
Quite frankly, I personally believe there's a perfectly mundane explanation, mainly because I can't imagine a real time traveler would be so careless as to walk down the street talking on a hand-held radio in 1928. But it's still pretty cool to think about.
-- Bob
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Then the horns kicked in...
...and my shoes began to squeak.
Google suggests (via my weak search-fu, which tells me there's probably more I haven't found) that it's a hearing aid -- and one link even provides pictures of a model that was manufactured before the film in question and has a battery pack that suspiciously resembles what I can see of what the lady is holding. Hearing aids back then resembled something out of a mad scientist's Victorian lab.
This doesn't explain why she's talking, but, I'm sure we've all seen the Crazy Lady talking to herself wandering down the street, I suppose.
--sofaspud
--"Listening to your kid is the audio equivalent of a Salvador Dali painting, Spud." --OpMegs
other thing of note, cameras in those days were LOUD. You knew when you were getting filmed.
She may have been talking to the cameraman, complaining about being filmed.
It's not like vanity is an invention of the last 50 years
-Terry
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"so listen up boy, or pornography starring your mother will be the second worst thing to happen to you today"
TF2: Spy