Yes, I read it as it ought to have been "Harriet Smith of Great Broughton, widow, the relict , John Platt, of Cupin Street, Carter...". Commas are very useful things, perhaps they charged for each? They do help the sense.
I'd guess John was a relative, if there's the name connection, but couldn't go further. Often a male relative seems to have been named alongside a widow or unmarried daughter ... sometimes I've found the husband of a daughter named, rather than her, in such issues.