Faster time:
To have days go quicker and have all the work done faster, hold the RIGHT MOUSE BUTTON.
Free resources:
Trade away all of a single resource by using the Merchant. You can keep trading it, even if you have 0 remaining. You can use this trick to get free supplies from your neighbors.
Quick neutrality check:
You can not send a Diplomat, Saboteur, Spy, or Merchant to a territory if it is not owned. If these options are not available for a territory, it is an indication that it is neutral.