No ideas for the viewscreen yet, but i started having a tinker with this scene, nothing really wrong with the purple lighting it's just something I never liked...
A side effect of this is that I discovered what appears to be a bit of an error - take a look at the colour of Kirk's shirt in each of the following shots - the other things in each shot seem to match up pretty well, colourwise.
I also noticed that the alignment of the transporter beam is pretty awful here - I haven't yet gone and checked other transporting scenes...Any thoughts?