I got an incomprehensible bug with geometry, I can’t even describe it, as if I have another layer above the main geometry, which is visible only at a certain angle, what is this bug and how to avoid it? And when I tried to fix this bug using DynaMesh, I just got holes around it, which raises another question, how to avoid holes? I am attaching screenshots, I also think it is worth clarifying that when exporting geometry to Maya, this bug is also visible.
Hello @Farmose,
It looks as if you have another mesh that is overlapping with the visible surface. It’s difficult to tell from the pictures, but it looks as if the mesh is also an open 2d surface, and not a closed volume. Trying to Dynamesh a mesh like this will produce the “swiss cheese” effect, where the mesh begins to disintegrate. Dynamesh requires a mesh be a closed volume with a degree of thickness to work.
Examine the mesh prior to Dynameshing. If your mesh is already one fused, contiguous surface, then it might be as easy as using the Subtool> Split> Split to Parts function to split any extraneous geometry into a separate subtool.
If , however, you have many sections of mesh that are not welded to each other, this will be untidy–it will split all those parts into separate subtools.
In this case, I would use a Tool> Polygroups> Auto Groups function on the mesh to ensure that all sections of mesh that are separate islands have their own polygroup. You may then be able to see the overlapping polygroup if you turn on polyframe mode. If you are able to then Shift-click on the offending mesh portion to hide it with one of the following visibility shortcuts–
http://docs.pixologic.com/user-guide/3d-modeling/modeling-basics/polygroups/
–you may then be able to use the Subtool> Split> Split Hidden feature to split the unwanted geometry into a separate subtool, which can then be deleted if you determine it is not needed. Once the problem mesh section has its own polygroup, it can be hidden, masked, or deleted with a variety of features.
Good luck! 
[p.s.] In the event that the normals for the overlapping geometry are flipped, preventing you from seeing it from certain angles, be sure to switch on Tool> Display Properties> “Double”. This will make all polygons viewable from either side.