Linear sampling causes strange lines

I have a rotating object and a bunch of tiles. When I turn on Linear sampling, the object is smooth, but when it moves, the tiles have white lines between them. When I turn on Point sampling, the tiles don't have the lines, but the object is ugly when it turns. Is there a way to make the object smooth and prevent the lines?

I'm guessing you're using the tiled background object for your tiles. If you use those for individual tiles, you'll always get lines between them on linear sampling, so it's best to use sprites for that purpose. Also, you should only use power of 2 textures with the tiled background object, eg: 32x32, 64x64, 128x128, etc...