Problems interpreting gram stain slide
The only reason that it shows both colors is due to imperfect manipulation while staining. You cannot count on the majority to determine the result of the stain.

In your specific case, rinsing or decoloration with EtoH was probably not done enough and safrainin wasn't completely eliminated.

The best way to be sure of the result would be to redo the coloring. 

A good tip while staining is to have duplicates or triplicates. 

Secondly, to answer what you said here: 


  I also understand why gram-pos appear purple, --that the crystal
  violet-iodine complex is retained due to thicker cell walls in
  gram-pos..... and thinner cell walls in gram-neg, so they are
  decolorized and appear the color of the counterstain.


Actually it is not only the thickness of the cell wall that will cause the bacteria to retain or not the crystal-violet. Gram positive bacteria have a plasma membrane then peptidoglycan on top while Gram negative bacteria have a plasma membrane, then peptidoglycan and another outer membrane on top. Crystal violet "sticks" primarily to the peptidoglycan. 

Decoloring will remove the stain on the outer membrane of gram negative bacteria. You were right with the fact that Gram positive bacteria will have thicker peptidoglycan.

Gram + vs Gram - cell walls http://www.diffen.com/difference/Gram-negative_Bacteria_vs_Gram-positive_Bacteria