I am new to Maya and am trying hard to develop good habits from the get-go. Often times when it appears
I have solid, symmetrical quad geometry and I try to insert an edge loop, the edge loop continues around the
object, but sends off errant edges. In the attached image of the staircase, I simply want to insert a line dividing
the staircas in half vertically, but the resulting loop creates a pattern of diagonal lines. To create the staircase I:
-made a single step
-duplicated with transform 6 times
-combined the objects
-merged vertices
-attempted to insert edge loops
I assume this will be an easy fix for someone more experienced, but it is driving me crazy. Any help is greatly
appreciated. 

Show the vertex mode.

Joojaa, thanks for the quick glance at my post. After hours of attempting to resolve this I got a hint from a side note in a 
tutorial I was watching. I believe the strange edges were being caused by shared faces. I was merging vertices without deleting
the faces they were sharing. Edge loops seem to be traveling the model cleanly now. In your experience, does this make
sense? Thanks.