Why doesn't the oxidation of cellulose oxidise all the alcohol groups, and how does it cause discolouration?
Well Noah,
Primary alcohols, in general can be oxidised more easily, if we are using suitable reagents like acidified dichromate/permanganate etc.

By looking at the reaction it looks like there has been some reagent used like lead teraacetate (LTA) or NaIO4, which attack syn, vicinal diols/(alpha)-hydroxy aldehydes/glyoxal to cleave the C-C bond and produce the oxidized product:


It has been mentioned elsewhere, that cellulose can be oxidised by NaIO4 into some carbonyl derivatives:

This reaction has been responsible for yellowing [at times referred to as discolouration] of paper:

These carbonyl groups arranged in some definite fashion give rise to yellow colour, sometimes called chromophore, which are any group responsible for proving colour to an otherwise colourless compound.