3D Terrain Tiling Graphic Artifact

I've created a terrain for a character (currently the 3rd person shooter tutorial model) out of 1X0.1X1 cubes/tiles. The tiles have different child shapes based on the terrain tile type (e.g. plains are just a textured tile, while hills are a tile with some ellipsoids poking through the top). For the most part this is running very well and serves my immediate purposes; however, at times I'll see black horizontal lines of varying lengths flicker momentarily as the player moves around. These lines are always where the tiles meet. All of the shapes were modeled using Unity gameobjects and are intended to be temporary until I get more experienced with Blender. Is there something I can do within Unity to correct this?

Based on what I've found in the forums I've tried the following -

1. ensure all of the textures in my materials are clamped...and then just repeated (no change with either)

2. I've ensured that the game is synched to the monitor refresh (no change)

I've read somethings about UV mapping, which I will explore as I get more familiar with 3D modeling, and suspect I will not be able to correct this issue until I can create terrain tiles with Blender.

Here is a portion of the scene in the Sceneview. I've selected a few of the tiles so you can see how they are interconnected -

Scene View

Here is a portion of the game view, with the black line showing just behind the player character -

Game View

Any suggestions would be appreciated.

Thanks, Joe