TCE is okay - no gaps.
Pressing "d" and "n" gives the following picture:
What exactly should be "snapped by distance"?
Two problematic points in the picture are actually two points each snapped togather with CTRL + T
Since I didnt understand what exactly needs to be snapped together by distance , I tried two things:
1) selecting each problematic "two point" and "snapping by distance" doesnt give any changes at all;
2) snapping both "two points" togather by "snapping by distance" also doesnt give any change;