All the best intentions can go to naught if you've committed any of these mistakes:
1. International Flight / Weather Roulette
Boats and planes to/from Yakushima get canceled pretty frequently. From June through October, expect about 9% of JAC flights (This is the JAL branch that flies to the islands around Kagoshima) to be canceled. Fog can force any flight to turn back before touchdown, and storm systems can create rough seas for several days.
I strongly discourage squeezing Yakushima into a packed itinerary without one or two buffer days between travel from Yakushima and any international flights. For domestic travel, JAL and ANA are usually very helpful rearranging flights, but international carriers are usually not so accommodating.
2. The Day Trip
Every time someone tries to make a day trip out of Yakushima, a fairy dies. Yes, if you calculate it perfectly, it may just be possible to take the first boat/plane in and high-tail it to the moss forest and back in time to catch the last boat/plane out. But this isn't an amusement park ride where the whole point is to stand in line for ninety minutes in exchange for 90 seconds of bliss. Don't you want to give the forest time to seep into your pores and infiltrate your spirit?
3. Accidental Super-Seclusion
Yakushima has one main road that follows its roughly 100-km circumference. To travel from the Northwest corner to the Southwest corner by public bus requires about 80 km of travel.
If you look at a map, you'll see that the Yakusiland, the Yodogo/Yodogawa Trail Head, and the Arakawa Trail Head for Jomon Sugi are closest to the town of Anbo, and Shiratani Unsuikyo Park is closest to the town of Miyanoura. Most people/restaurants/shopping/buses are to be found on the EAST side of Yakushima, clustered around the villages of Miyanoura, Koseda, Anbo, and Onoaida. If you stay in-between villages or on the more remote WEST half of Yakushima make sure you understand the bus schedule and have a plan for food and transportation.
4. The typhoon/monsoon experience
There are typhoons and there are Typhoons. Some of them aren't too strong and, to some extent, Yakushima can be nicely calm just after a typhoon before most of the tourists come back. However, if it's a strong typhoon, it would be reckless to put yourself in danger by leaving mainland Japan. With very few exceptions, outdoor activities are canceled when a typhoon is imminent, and roads usually need to be checked once the winds have died down. Typhoon season lasts from July through November.
Monsoon season lasts from mid-May through the start of July (usually) . As the monsoon season picks up, torrential roads make trails and mountain roads unsafe and hiking is often canceled. However, this is also the sea-turtle egg-laying season, so many people are happy to take the risk for a chance to see the sea turtle miracle. (Reservations and/or transportation arrangements or accommodation near an egg-laying beach recommended.)
Before you go thinking that you can avoid all storms by visiting outside of monsoon and typhoon season, note that we can have blizzards in the mountains from November through April.
5. City Slicker Nostalgia
You want your 24-hour ATMs, wifi, western toilets along the trails, a taxi to take you a kilometer, vegan or gluten-free meals, credit-card purchases, and a guarantee that you can do a certain hiking route in a certain time frame. If you want all that, you're going to have to book Sankara. (No disrespect for vegans! Veganism just isn't well-known in this culture with only a tiny strip of arable land.)
6. ¥100 Rain Gear
Why spend all the money and time to come to Yakushima and not put out ¥1500 for two-day rain gear rental?
7. No Licence = No Car Rental.
According to the JAF website at time of writing, regular drivers' licenses from Switzerland, Germany, France, Belgium, Monaco, Estonia, and Taiwan are valid in japan, BUT YOU MUST CARRY AN OFFICIAL TRANSLATION (available from JAF: https://english.jaf.or.jp/use-jaf-more/drive-in-japan/switch-to-japanese-license ).
Many other countries are party to the Geneva Convention. If your country is not listed above, but is part of the Geneva Convention, in your home country, you can apply for an international driving permit. (The process is usually fast and painless, but you CANNOT DO THIS IN JAPAN.) You'll need to carry this, your passport, and your driver's license to drive in Japan.
Bonus: The no-show
By canceling without notification, you could be endangering the lives of others.
Therefore, as a matter of courtesy and safety, please, always contact your host when you need to cancel (rooms, tours, car rentals, etc.). Otherwise, not only is your host losing money on your booking, they are often very worried that you are lost in the mountains. Hotels will often call the police to instigate search/rescue procedures when guests do not return. Other times, hotels hesitate to call the police because they've had other guests fail to show up and assume it's nothing.
Anything I've forgotten? There's a lot to do on the island, and even without a solid itinerary, you can have an incredible experience. Just try to avoid the above mistakes!