Hello!
I’m currently trying out a tutorial I found on YouTube, creating earth in Blender. I’m finished and want to render out the animation, but when I do, these wierd pixelformations appear! I’m using the Blender Render engine (cause that’s what the tutorial said).
Would be very greatful for a quick fix! 
Looks like you are affecting the normal bump of a material. As there seems to be a relief effect (shadows) occuring. This doesn’t look like a rendering artefact to me.
I have to agree with 3point, assuming you are talking about the water. If my guess is correct what is causing the bumps was meant to make the surface less uniform (read: simulate waves), so something could have gone astray in the node/material section.
