generally blending modes and transparent gradients are a mixed bag when exporting pdfs.
I find it's a good idea to rasterize the transparency before exporting. You can do this by selecting your partially transparent layers and the layers that they are on top of and go Object->flatten transparency. Obviously these parts of your file will no longer be vector and are considered raster images, this can increase your file size. The flatten transparency option does let you choose the resolution it flattens at.
NOTE you will want to duplicate your art/layers that you are flattening before flattening if you want to retain future editing abilities of your shapes and opacity/blend modes.