Just to chime in on the Horizontal/Vertical thing...
It could be that the badge/symbol is oriented one direction, and the actual ID portion is the other way. I've seen official ID's like this before. I'm sure we've all seen them in various Movies and TV shows. Agencies like the FBI or CIA would probably use something like that. Their badge on one side and their ID on the other side but turned 90 degrees.
Hence, Sulu is flashing the "badge" to the jailor while the interrogator with Chekov is reading his information.
(Though a GIS of "FBI Credentials" doesn't seem to support my hypothesis. And has probably flagged my computer by the government! >.< )
Just my 2 cents.