I recently drilled 6mm pilot holes for anchors in a 6in interior concrete wall with a thin plaster coating in my apartment. After drilling and a day or so later, I noticed a 5 ft long vertical crack on the OTHER side of the wall from which I was drilling. I noticed it from a bulge in the plaster. How serious is this?

https://drive.google.com/open?id=0B4ZIsSI9G4WlOUs3bzZaUGFHZmc

https://drive.google.com/open?id=0B4ZIsSI9G4WlOUs3bzZaUGFHZmc

That jut looks like crack in the plaster to me. A settlement crack that has been repaired before. Probably there before you drilled for the anchors you just didn't notice it.

An interior wall in an apartment made of concrete? How sure are you that its solid concrete and not block? If its not a load bearing wall no big worries.

If its Europe... its actually a type of rough unglazed terracotta brick or block that's got a sand loaded plaster (almost like a real stucco that's cement based).