Are the "first watchman" and "watchman" in Much Ado About Nothing actually the same character, or are they different?
As Shakespeare doesn't pay much attention to minor characters, I couldn't figure this out by myself.
The Folger edition identifies the Watchman lines with various characters, including First and Second Watch, and George Seacoal (whose name is mentioned but not listed in the dramatis personae).
It's an editorial decision based on their analysis of the style and subject of each line. The lines are identified just as "Watch" in the First Folio.
I'd say it's not so much about Shakespeare's attention to minor characters as the sloppiness of the original editing. The First Folio was assembled from a variety of not-entirely-reliable (and probably not-entirely-legible) sources. The original performances presumably had definitive answers to these questions, with the author present, but that would be lost over the next couple of decades before the Folio was prepared. (There was a Quarto edition much earlier which was likely used as a key source for the Folio.)
You can take the Folger editors' word for their decisions, or make your own. Since the play identifies two watchmen by name (Seacole and Oatcake), who are different from the First Watchman (who speaks those names), you've got flexibility to determine for yourself who is who. I don't believe that a close reading would support giving all Watchman lines to be First Watchman, though I haven't done that analysis.
(I note that the Folger edition takes one line labeled as Watch 2 and assigns it to Seacole, then gives a different Watch line to Second Watchman. So... yeah.)