I clicked more than usual last season, but I regularly encountered a problem, all the cities in the country I was in had the little V to say that I had already explored 100% of the cities, while several had not yet been explored ... This season I should have less trouble as I'm in a gigantic city, but it's a bit of a hassle ^^'.

The ✔️ tick indicates that the city has been visited... by at least one manager in the country, not necessarily by you.
This allows you to make an informed decision about whether or not to go and prospect in a city where there will be competition.

Blagoje Vidinic: La coche ✔️ indique que la ville a été visitée... par au moins un manager présent dans le pays, pas forcément par toi.
Ça permet en toute connaissance de cause de choisir ou pas d'aller prospecter une ville où on aura de la concurrence.

Hmm no, or there's a slight bug in that
I can assure you that, as I'm in the same country as a fellow member, the town where he's currently based is not ticked.
Similarly, last season, I went to retrieve a detection made by a friend and I can assure you that the remote village where he was was not ticked. That would have helped.

Maybe there's a slight bug with that, or maybe it's being misinterpreted.

This only appears on the page of the last player detected in the city in question: all the cities checked have been visited.

Blagoje Vidinic: Cela n'apparaît que sur la page du dernier joueur détecté de la ville en question : toutes les villes cochées ont été visitées.

And how do you explain the fact that from one day to the next the cities were sometimes ticked and sometimes not?

Change of town >> the ticks belong to you
List of towns below the last junior detected >> the ticks are shared