Yes, you are going to have serious problems with that geometry. What you have done is taken three cubes, elongated them, then bent them into horseshoe shapes. This is an acceptable processes. The mistake is made when you intersected them together to form a star shape. The star is made up of intersecting faces, some of them are partly passing through others, at all different elevations because the shape is domed. It's going to cause rendering problems when Maya (or any software really) because the software doesn't understand what it needs to drawn on top. It also makes editing the shape a fairly complex process.
Going over what needs to be done is too complex for the forums, so check out
http://www.digitaltutors.com/ for some excellent modeling videos
-Avotas