The paper work goes in the bin at the end of a flight? There are certain items tht need to be kept for serveral months...not quite sure how long , among them the flight plan and the voyage report.
In my company we have to do a fuel check every 30 mins and log departure clearances taxi instructions and all comms above FL100. Its a good idea since you have a record of the flight come any disciplinary action for any reason..ie alt busts etc etc.