For the dirt, I'd just pick a grungy brush and try a dark brown or black colour with the layer blend set to Multiply. Just start painting around and see how it looks.

I think individual paving stones would look much better, and you could paint some dirt in the cracks between and maybe have it edging out from the cracks onto the stones.

I hope it wasn't a huge amount of work to create the mosaic effect (I didn't have time to read through the tutorial in detail, but it looked complicated!) Still, it's always easier and faster once you know what you're doing.

The only other suggestion I have, and this is entirely a personal taste thing, would be to desaturate the colours just a little. I'm not sure what overall effect you're going for, but I kinda feel that if it's a rather dirty mosaic floor pattern, then the colours might be a little muted and faded, whereas yours are quite bright and vivid. However, that's perhaps exactly what you want, in which disregard this suggestion!