The "avisos" or "Wanted" posters invariably announce the reward in "pesos". Although this brings to memory the post-independence Mexican peso, the name "peso" ("peso duro", etc) was used for centuries in the Spanish colonies for the Spanish Real or "piece-of-eight", and California was not an exception.
The use of "centavo" as a fraction of "peso" is anachronistic, as this was an example of post-Napoleonic decimalization (the colonial Spanish peso was divided in maravedis).
Diego lands in 1820 and there is no indication of how much time passes, but there is a problem if the time runs more than a year into 1821. In 1820, California was under Spanish control as part of New Spain. The Spanish had established missions, presidios (forts), and pueblos (towns) throughout the region. However, just a year later, in 1821, Mexico gained independence from Spain, and California became part of the First Mexican Empire.
Throughout the series, the lancers and others are seen shooting their muskets multiple times, the problem is that muskets are not semi-auto. The first semi-auto rifle was first introduced in 1885. The muskets they use are single shot only and would take the lancer approximately 1 minute and 20 seconds to load and shoot each time. This would give Zorro ample time to always get away unscathed and without much resistance.
Spanish Colonial California used the Spanish Dollar or Real not the Peso. The Peso, actually the Mexican Peso was introduced to replace the Spanish Real in 1863. America bought California in 1848, so the show has to be set earlier than that so the Peso would not be in use.