Your 3 Pits I assume are initially one surface or are they 3 separate surfaces - either way the issue that you are seeing is that each of those three surfaces have their own boundary line that is added to the surface as a Surface Boundary not just a surface member / breakline. Then you use those three boundaries as "clipping" lines to patch them into your master surface that also has its own boundary by the looks of it. That then means that the three boundaries around your pits become "holes" in the master surface rather than additions (the outer most boundary becomes an island, the next boundaries inside become holes, the next boundaries inside the holes become islands etc.
So: the if your Pits are separate surfaces - add a Surface Edge Breakline to constrain them and add that as a Surface member not a Surface boundary. If your Pits are part of the same surface then having them defined as "islands" each with their own Surface Boundary object will cause you to get holes in the Merged Surface. So I would define the Pits as 3 separate surfaces and have them edged with a Breakline and not a Surface boundary.
When you patch the surfaces together, if you Patch the Pit 1 into Master Surface - and use the Surface Edge Breakline of Pit 1 to create the Hole into which Pit 1 is patched - then that will clip the triangles of the Master Surface along that line. You can still get flags in this case, because the Master Surface may not have exactly the same elevations as the Patched in Pit 1 - To avoid that you may want to create an offset line of the Surface Edge breakline for Pit 1 at say a 1' offset and use that to clip out the Master Surface as you patch in Pit 1 - that way there will be a 1' zone across which triangles can form between Master and Pit 1 to eliminate the Flags that you are seeing. Repeat this for Pit 2 and Pit 3.
I can take a look at your file next week when I am back at work on Weds - but I am pretty sure that this is the issue.
Alan