Is there any permanent progression in this game?

[minus]

Character unlocks, talents, certain pieces of equipment, anything?

[Let's Get Visibly Upset!]

Upgrades to your town allow you to make recruitable heroes more powerful at an earlier level via the guild + blacksmith

[minus]

Good to hear, thanks for the info!

[yajiu]

Trinkets, though I believe you have to win the fight where the character dies and pick it back up in order to keep them.

[Satoru]

Your town has various upgrades that you'll need to level up your heroes gear and skills

You'll also be upgrading a lot of the stress relieving buildings to better mange teh stress levels and insane quirks your party picks up over time

[RexIvan]

Originally posted by yajiu:

Trinkets, though I believe you have to win the fight where the character dies and pick it back up in order to keep them.

Not so. Even if your entire party wipes, you can still gather the trinkets off their dead bodies from the graveyard.