I don't know what they have learned, but I know what I hope they have learned:
1-Name and Marketing. They need to get a good name that doesn't confuse potential buyers and get a proper marketing campaign.
2-Launch games are important and should show something that couldn't be done on their old console. New Super Mario Bros U was not a good choice for a launch tittle.
3-Do not rely exclusively on "gimmicks" to sell your machine. If they work, it will help push more consoles but if they fail you'll be in a very difficult position.
4-Price matters. And they should have learned that with the 3DS. But with that said,
5-Sell your consoles for a profit or a very, very small loss. Sony and Microsoft have other divisions that can offset the losses of the hardware but Nintendo doesn't, so they should try to avoid this strategy.
6-It is imperative to avoid software droughts. I do really think that they have learned this lesson but I also fear that their answer to that problem won't work. Having a unified architecture and OS will allow their 1st and 2nd party teams to develop their games faster but if they don't expand their current teams and fund new ones they will still face droughts.
6-It is important to have a third party friendly console and try to get them onboard, but it would be stupid to rely on them. It's your job to sell the console, and only if you do that and if you do it well that they may come back and launch games on your console.
Please excuse my bad English.
Currently gaming on a PC with an i5-4670k@stock (for now), 16Gb RAM 1600 MHz and a GTX 1070
Steam / Live / NNID : jonxiquet Add me if you want, but I'm a single player gamer.