While the makeup of the Signoria is shown to be relatively static, in fact, members served only two months.
During the first season, the dome of the Florence Cathedral is shown under construction except for an outbreak of plague and Cosimo's exile, and never as completed. In fact work continued the whole time, even during Cosimo's exile and was finished in 1435. It was consecrated on 25 March 1436, New Year's Day under the calendar in use by the western world at the time.
We see some constructions built indeed later than the described era (XVth century): the dome of the San Lorenzo Basilica, completed by 1604, the Vasari corridor (1565) in Florence, as well as the Venetian Church of Santa Maria della Salute (1681).