You wouldn't have much gravitational shear (no more than the inner planets already experience from their own star). You could really screw up the orbits of everything in the system though, including the star(s) orbit around the galaxy.
You would also sweep a chunk of space 15 light-minutes in diameter as you fly. (A single sphereworld would fill the space between earth and the sun). Perhaps you could install planet busters and increase the value of your sphereworld as you absorb more mass.
The internet on a Sphereworld would be really laggy, seing as even a fiber-optic connection would have a 45 minute ping time
to the other side of the world.
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[This message has been edited by suicide_junkie (edited 27 July 2001).]