I'm in the second mission and, after looking at a note that says that a guy named Arthur is waiting for a girl named Gwen by the end of the bridge, I decided to go check it out and found what I assume is Arthur dead and right above him is writing on the wall that says "Darren + Gwen." What? The note said that his name was Arthur. I was just wondering if anyone knows something that I don't. This may be a nitpick be I'm curious nonetheless .

Maybe Gwen was two-timing Authur?

maybe he found out gwen was seeing darren and killed himself?

I suppose, but I don't recall seeing anything he could've killed himself with. I'll have to re-check.

I noticed this too. Just seems to be one of many "little mistakes".

How do you figure it's a mistake? Also, what are the other things you consider to be "little mistakes"?

If you think something like this is a mistake then ask the developers over at Twitter.

Ok, so Darren fancied Gwen, found Arthur waiting for her, killed him, wrote on the wall... Something like that?

Maybe not the ideal post this in, but seemed silly to make one just for this... And it seems like a real mistake.
Just outside Granny Rags' front door, on the "rubble" to the right, where there's a radiator, a chair, and an inexplicably burning stove, there are two invisible pouches on the ground, one with 20 coin, one with 10. They aren't visible with darkvision, and by the positioning seem to be on the ground, or maybe even in the air, rather than stuck in it somehow.
Makes me wonder if there are any more invisible items around.

Maybe Arthur killed himself when he saw the graffiti.

Or maybe the body is just a hobo and the outsider added the grafitti to manipulate you into entertaining him by killing Darren, which is actually working on helping orphans.