Why?

Open canavs work, where unstitched canvas is visible, requires the stitcher to take extra care to hide travel threads.

When I see a piece that has this mistake, a glaring, obvious mistake in the midst of an otherwise well stitched piece I just cringe.  Why did the stitcher do this?

Why?

The arrows point out travel threads in this Milanese Pinwheel stitch and mar the beauty of this stitch.  Why is the travel thread only visible for the pink thread?  

Perhaps the variegated thread was stitched first (which it should be because it is lighter in color and if pink thread was pulled under the lighter thread it would be seen from the front) with all stitches going down into the center hole, which allows the stitcher to pivot to the next stitching area and hide the travel thread.

How are the pink stitches executed?

Probable Stitch Execution

I can’t be completely sure, but this is how I think it is stitched, with the arrows showing the stitch  direction.  This leads me to think, Be Consistent!

Probable Stitch Execution of All Stitches

All stitches for each Milanese should be executed in the same direction.  All long threads going down into the center hole, which again, allows for a correct pivot to the next Milanese stitch.

If you must change the stitch direction - and it really should be for a very good reason, then placing a tacking stitch underneath the pink thread, between Milanese Stitch units, is essential to hide the travel threads.  You may have to push the pink thread aside to access the canvas holes to take this tacking stitch.  Here is where the tacking stitches should be taken:

Where to Place Tacking Stitches

Each of the black lines indicate where a tacking stitch should be placed under the pink stitches.  Pink is much darker than the light variegated thread, so tacking stitches need to be made under the pink thread.  Place the stitches below where the variegated stitches cover the canvas, so that when the thread is pivoted to take it to the next Milanese Stitch area, the travel thread will lie behind the variegated thread.

One of these two simple steps - maintain a consistent stitch direction with all long stitches going down into the center hole or place a tacking stitch - will easily fix this problem.