Okay I Used Transwater This Time
Here are three screenshots. In your original five I actually wasn't sure where the problem was in a couple of them, but I could see the problem in the two shots taken from in the water near the crate. The last of your screenshots illustrates what the player sees when they cross one of the 4096 unit map boundaries.
In the water near the crate:
http://quaketastic.com/files/screen_shots/bre01shot1.jpg
http://quaketastic.com/files/screen_shots/bre01shot2.jpg
As you can see there are no problems.
Crossing the 4096 unit limit (this is normal):
http://quaketastic.com/files/screen_shots/bre01shot4.jpg
I have no idea if saving the map in Netradiant magically fixed something, but I was too lazy to download the texture wads you used, so I had to load the map in Netradiant so I could change them to regular Quake textures.
I used the Tyrutils v.014 qbsp and vis to compile the map.
I don't see any reason to give up on the map at this point. You do need to move the map away from the 4096 boundary. The map is basically one large open area, I doubt you're getting much benefit from detail brushes, but from what I see they're not the cause of any problems either.