Are you using CMYK color profiles? Photoshop almost always defaults to an RGB profile (a really wide, on screen color gamut) Print devices only use CYMK, a much, much narrower color profile. You shouldn't be able to print a true lime green at all really, or a deep navy blue (usually comes out purple) Bright orange (might appear brown), anything neon..
As for your greys, make sure you use a pure halftone of black, 15% black, 45% black etc. This way they have no chance of swaying in color.
If you can, design in InDesign or Illustrator, these program were made for print. Photoshop, was made for editing photos for a developing print process - Or web design.
I hope this helps a tad bit!