Interesting, I didn’t know this expression. Without the translation of “We all make mistakes”, I would have expected it to be “Tutti fanno errori”, and with the translation perhaps “Facciamo tutti errori”, or maybe even “Facciamo tutti degli errori”.
I think the word order is for emphasis on “tutti”.
Ciao sindaco. Fanno is more “they” than we no? Me too, I’m always tempted to put the verb first and add gli, but evidently not. So I tend to go with Tutti facciamo errori.
Stammi bene eh!