Judging on what you know, what would be your best way to fix these "offending" edges?

They were created by the wrong use of Extrude Edge and Merge Vertices actions so there we have an example of wrong non-manifold geometry. If i were to Bevel the border edges of the face, script editor will tell me that it can´t since it has found a non-manifold vertex (actually lots of them).

What would be your approach to fix this problem then?

Thanks!

Don´t know what non-manifold means? Click here!