These tips are fairly general, but should focus on shaving a few seconds here and there for leaderboards. This guide does not take into account token collection or maxing out bonuses from detention, bribes, or anything else*--these tips only focus on getting the line moving as fast and heartlessly as possible for maximum salary ($5 per immigrant processed).

*NOTE: As Steam user "Angel Melody" notes below, these tips only address speed and consequently fail to take into account the thematic aspects of the game. Use them for leaderboard play, but know you may lose some of the message of the game if you were to apply all the tips here (and in the comments) on your first run.

Until a certain point in the game (and for the first two of each category of endless), you are free to stamp denial for any discrepancy without having to point out said discrepancy from the rulebook. For example this means if someone is 190cm but their ID card says they're 145cm, or they say they're there to visit but have work papers, you can stamp deny and hand them their papers back without having to look at the rest of their stuff. This can save a ton of time in the early days of the main game and on endless events.

EXCEPTION - You must point out the discrepancy for anyone missing a passport. Unfortunately, if you do that, then they may provide you with one, forcing you to inspect it. Remember, it isn't your job to help them figure out the documents they need to hand you. A missing entry permit or ID card in early game warrants a quick stamp and "next!"

If a wanted criminal wants access, you are free to point out (or not where applicable - see above) the discrepancy and deny their passport. Just because you have the option to detain does not make it mandatory. You only get five seconds back for detentions in timed-endless mode and it doesn't come out to a net gain waiting for the soldiers to remove the detainee from the booth. This applies to invalid ID numbers, wanted criminals, forged seals, and anything that requires further verifying of identity. That said...

Names different? Fingerprints don't match? Height is off? Pointing it out and then fingerprinting/searching them takes forever! If early game, just deny and send away. If in the later game where a denial reason is necessary, point out discrepancy but refuse to fingerprint them. Ain't your job to care if they wore tall shoes that day. Stamp deny and get that line moving!

• You can place the passport in between the two stamps to speed things up (example below).
  
• A denial overrides an approval, but not vice-versa--regardless of stamping order or number of stamps. So if you approve and notice something at the last second you can fix it as long as you haven't returned the passport. If you have returned it, you must be able to point out a detainable discrepancy without the passport or take the penalty. In the example below, this immigrant would be denied.
  
• The immigrants seem to always finish their reason/duration of visit speech before leaving, so that'd be the upper limit of how fast you can deny/approve an individual immigrant.
  
• Hotkeys work in endless mode, presumably whether you bothered to unlock them or not. So you can [TAB], [SPACE], and double-click. Please correct me if I'm wrong here, as it is an assumption.
  
• User Jack Attack! commented that he approves the passport initially, then stamps the deny stamp when a discrepancy shows up. This can save you a few seconds given point two above.