I believe this is commonly known as alpha clipping or edge clipping. It's likely Hournces would have had this issue as well with the material in his tutorial, he simply just doesn't show that scenario. I can't say for certain, but this tutorial may have some solutions for you.
Hey all, So I'm trying to teach myself how to make my own waterfall by stumbling through the material editor and the particle system editor. Here's something I have for the mist: As you can see, where those particles intersect the BSP, obvious hard edges can be seen. I followed hournces' tutorial here to the letter:…