Quake3World

That's an old error you'll often encount with ATI graphic cards. There's pretty much nothing you can really do about it, just ignore these lines or get used to them, as there are very few maps out there (compared to all Q3 maps floating around the internet) that specifically dealt with the ATI problem towards skybox. In all the other maps you'll see these lines no matter what. Sorry, I as an ATI GPU owner can't stand that problem myself.

The map looks cool, actually. Do you have larger pics of it?

There are some work-arounds that requires you to set up a portal sky or a hemisphere sky shader. There were a few tutorials posted a long while back. Also -skyfix, though it depends on the skybox.

Oh no guys. Im pretty sure there exists dll library to fix it. I'm so pretty sure because I have one in my folder Just to find it...

Well, there is that fix I was talking about. Put it into main folder (Quake III Arena) where also baseq3 is located and your problems with beautiful skies will be gone
http://www.ulozto.cz/7020690/openglfix-zip