Alistair has a scar that stretches over his left shoulder from an emissary in the Deep Roads. When that nasty, blight-acid hit him, he got scarred there because healing can't do everything and by the time he could get healed, well... the scar was already there.

Asaanelain has a lot of scars. He's missing both eyes in true demon hunter fashion, his skin has multiple claw marks, and his wings are permanently tattered thanks to old torture.

Kalecgos is a little too magical to have scars. He has been wounded, but just being draconic means that most of his wounds heal very well.

Edgeworth has a few lines across his chest and back because Franziska is nothing if not consistent, but they've healed very well and are only barely visible, thanks to how pale he is. He has a few other scars but nothing really bad or noticeable.

Reiner has no scars until after the end of the series. Titan healing, yay?

You have an Edgeworth? did I know you have an Edgeworth? darn it now I want my franziska muse back!

I do have an Edgeworth! I also have Greg!

Oh wait, I forgot one.

Haytham has quite a few scars, but the biggest one is one in his torso where he was practically run through. It got infected and he was lucky to live through it. It canonically causes him a lot of pain but he's good at acting like it doesn't.