How I'd Improve The Show
Firstly, this show had great potential. But it was too formulaic and too episodic.
It's greatest feature was the way history was regularly changed each episode (that was actually a new and interesting idea for a time travel show).
In season one, Rittenhouse were nothing more than a powerful secret society who had existed for centuries, but in season two, they suddenly became a secret society whose power was entirely built on time travel (their leader was even brought to the future from 1918). That felt like the writers making it up as they went along. And who the fuck was he anyway? They never explained anything about why he was supposedly so special? Then they just shot him because they clearly didn't know what they were doing. LOL
Here's how I'd improve the show:
I'd start the show in a post apocalyptic world of poverty, gangs, and mayhem. The time travel team are in their bunker, locked away from the world outside. The reason the world is a mess is because Rittenhouse has invented a time machine and taken over the planet, slowly but surely making themselves overlords via sleeper agents throughout time.
But then, Connor Mason also invents a time machine. A team of specialists, led by Mason, establishes the bunker and recruits the people they need (the normal team plus a few security and staff). Mason realises that the world is a mess because of these other people (Rittenhouse) having their own time machine. He realises the world wasn't once like this.
The team are now assembled and have the tools to try and fix history.
Plus, instead of having a different era each episode, I'd have more character studies and episodes that don't even involve time travel. Use it sparingly. Make it matter.