Sfdebris.net

#1: Make sure the locals believe in concepts such as the rule of law and innocent until proven guilty, and that they don't have such insane laws on their books that a member of your crew might be in danger of summary execution for picking their nose in public, jaywalking, or ignoring a Keep Off The Grass sign.

#2: Make sure your horndog of a first officer has the good sense to use condoms and is not going to bring back some exotic and extremely unpleasant form of VD.

3. Ensure that shore leave is rotated between crew so that the ship is not left unmanned and undefended while everyone is away, and that at least 1/4 of the senior staff remains on board, so that somebody is on duty with a clear chain of command at all times.

4. Consider changing passwords when a senior officer or noncom goes on leave.

5. Properly scan the atmosphere of the planet for any hallucinogens or other chemicals that will cause the crew to behave oddly. If something unusual is found then investigate further before commencing shore leave. Be sure to account for all species serving aboard your ship.

6. Schedule leave with the local administration and assure that you are aware of other species who will be enjoying the location at the same time. If rival species have shore time scheduled consider rescheduling your stay for another time or on another part of the planet.

I'm going to ruin this chain by being a spoilsport: Use common sense.

Because that ultimately is what every example here is. Common sense. Maybe Archer has an excuse as he does have inexperience and probable nepotism on his side. But someone like Picard or Kirk who have decades of first-hand experience as well as a couple of hundred years of OTHER captains writing out reports and telling stories of their adventures, there is no longer any excuse.
Check the weather, check the laws, check the society and culture of the people, and check the flora and fauna. In any real universe Picard or Kirk would be sued for negligence at the amount of redshirts that get bumped off under their watch.

TV suspension of disbelief rules: no such thing as alien microbes/viruses/animal bites/space rabies (unless the plot demands it). which is perfectly fine. not going to nitpick.

Real world: who knows. the bacteria in alien yogurt might equal ebola.

You're future astronauts, you should be trained/screened to maintain sanity on a metal tube for months/years on end. Current astronauts/cosmonauts can do it now on the ISS which is a closet compared to the NCC-1701.

Actually given the stories I hear of shore leave from my friends in the navy and marines sci-fi comes across as kinda tame. No one in star trek has ever stolen a cop car or set fire to a bar...

Not Star Trek, no. Farscape however...