Flat surface in blender mesh

Hi Guys
I’m trying to create a simple Snooker game in unity, and everything was going great until I tried to model my own pool table in blender. I managed to import it to unity and it looks ok, but when I started the game, all the balls started moving slowly in different directions, like if the table wasn’t flat. I tried to fix it in blender (selected all edges of the table top, and then scaled it to zero in z axis), but it didn’t help. I’m new to blender, so I could make some errors in the model, but I can’t find it. In blender it looks perfectly flat.
Please help. What should I look for to fix this?

It seams that problem was caused by starting position of the balls. I was setting them by hand. Some of them probably overlapped, what caused physics to go nuts. Setting balls a little further from each other, helped!