What you are seeing I think is normal behavior (hard to be sure with just two screen images, but there is nothing unusual from what I see).
From what you are saying you used photographs and the ReCap 360 cloud service to turn photos into a 3D model. That photo-to-model service generates a triangular mesh with a texture map applied to the surface of the triangular mesh. Triangular meshes are solid -- meaning they have a surface. The precision of that surface is defined by the number of vertices and the number of triangles that you have. When you zoom in between the vertices you still see the surface of the triangle that spans between the vertices, but the precision of that surface is limited by the number of vertices.
You then appear to have exported your 3D model from the ReCap 360 cloud service to a desktop file. Specifically it looks like you exported to the RCP file format, which is a laser point cloud format. Laser point clouds are just that -- a collection of 3d dots in space. Note that they don't have a surface. So while you started with a solid surface as a triangular mesh (with texture mapped color painted on that triangular mesh surface) when you exported to a RCP point cloud you only have the *vertices* of the triangular mesh stored in the RCP file. Each vertex point is infinitely small position in 3d space.
You then loaded the RCP file into the ReCap Desktop application which is used to work with laser scans and RCP data. Laser scanners only scan a cloud of discreet unconnected infinitely small 3d points in space and don't generate a surface as we've said.
When you are zoomed out the distance between each of the 3d points in the RCP file are very close together and they appear as a continuous surface, much like a cloud looks solid from the ground. But as you zoom in on those points you can start to see that there are gaps between each point (what used to be the vertices of the triangles in the original mesh).
The other thing that appears to be happening is that as you zoom in or get increasingly closer to parts of your object some of the points are "clipped" - in other words they actually end up behind the camera. The analogy being that if you get closer and closer to a cloud eventually your head ends up inside the cloud and you can't see behind your head. The water droplets behind your head are "clipped" from your view.
This was a long winded answer, but the simple answer is that you probably wanted to work with a solid surface and as such you should have the ReCap 360 cloud service export to a mesh based file format such as OBJ or FBX. You should also use applications that are meant to work with mesh data (and there are hundreds of them). OBJ and FBX are both open standards to which many manufacturers have software to deal with them including editors, viewers, decimators, painters, etc. Autodesk's Max and Maya and even AutoCAD and MeshMixer can all work with mesh data.
You might find the Autodesk Labs prototype application called Autodesk Project Memento to be interesting -- it works with OBJ data and lets you clean it up and 3D print it.
-Brian Mathews