First, I'm assuming you created all in AI and di not import anything from a raster app like photoshop.
If you're seeing any sort of box - stroked or filled - when shoeing the transparency grid, it would indicate that you have a fill or stroke applied to that box, in this case white. Select the box and take a look at the stroke and fill colors on the bottom of the tools pallette. They should be None - box with red line through it.
I'm assuming that this box you're seeing is either a text box or one that was created by grouping several objects.
Using OSX 10.3.9 on a G4