Hi Marcin,
A couple of observations...
1. The density points that you supplied all have a value of 0.0 so the node placement algorithm ignores the density.
2. You supplied hard points over the entire domain, again with values of 0.0
3. The default edge length you supplied is so very small (0.2).
This all over-constrains the node placement algorithm.
If you remove your hard points and density points and set the default edge length to around 2000 you will generate a better mesh.
Now on to your original problem...
Here is your original mesh showing the element IDs.
You can see here that the blue triangle is not actually defined as an element (It's a triangular island). I suspect that this is what FUDAA is complaining about. The old Blue Kenue version you are using (3.1.3) has a bug that allows this to occur.
One solution is to define a higher density at the head of your penninsula. Set the edge length to something less than the overland distance from coast to coast.
Martin