What are the take aways from the Wii U's fastest seller? 

I think Nintendo firstly needs to understand that the Wii U is its own audience, it's definitely not the Wii. Wii U owners are Nintendo fans, BUT there's a kicker here. 

They want BIG Nintendo experiences on their Wii U. They don't want things that feel like 3DS or Wii experiences running in HD. This is why I think NSMBU, DKC: Tropical Freeze, and Mario 3D World didn't do quite as well as maybe some people expected. DKC and Mario 3D World certainly are very good games actually, but by the same token I think Nintendo could've pushed themselves a bit harder with both of those games in certain areas. 

Contrary to what Nintendo thinks too, I don't think using the GamePad well is all that important. But Nintendo should focus more on fun and deep (no more mini-game nonsense) multiplayer games with solid online interfaces. Mario Kart 8 totally gets that. 

Nintendo's best bet I think from here on out is to make sure their remaining "big gun" software like Smash Bros, Zelda, Metroid U, even Bayonetta 2, etc. are BIG experiences. Don't cut corners on the graphics (sorry but Wii graphics in HD isn't good enough, flex some of that hardware muscle), the online, the presentation, the music. MK8 gets all this right. 

If anything maybe the past console Nintendo can model the future of the Wii U after (or at least try to) is the N64. The N64 did not have very much third party support at all, but many Nintendo games were really robust, big experiences that pushed the envelope of their genre. I think that's got to be Nintendo's play now. Wii U is not going to have the N64's userbase, but perhaps Nintendo can score some solid software sales for certain big titles, just like the N64 managed to do. 

That the "couch experience" crap is total BS.

-in a singing voice- someone doesn't have freeeeeeinnnds 

User was moderated for this post - Conegamer

They can learn that if they make a good game, putting enough effort into it - that game will sell well.

Meaningless stuff like console power and the gamepad don't mean anything to Nintendo fans without the mainstay games to back it up. This is a good start to get Wii U back on its feat. The Wii U needs more of the powerhouse games, less phoning it in with ports and mediocre Mario games (the last exceptional Mario game being Galaxy).

They need more of this just to be at Gamecube or just a bit higher than Gamecube numbers. Nintendo still needs a miracle.

The importance of BUZZ and good marketing. Don't repeat what happened with 3D world, with the shitty debut trailer and terrible marketing

At least we can say, next week we'll see Mario Kart 8 #1 on the sales chart overall.

Mario Kart 8 has higher end graphics and also has the best soundtrack in the series and some pretty epic new tracks. It just feels like a game that was made from the ground up for the Wii U. NSMBU got everything off to a bad start.

Mario 3D World partly by Nintendo's own marketing incompetence just looked like they were reworking the 3DS game.

People wanted Galaxy 3.

For Zelda I hope Nintendo realizes people want a big epic Zelda here, not A Link Between Worlds 2 or even Wind Waker 2. Nuh uh. Not flying Nintendo.

X and Bayonetta 2 would be better served by making those games as epic as reasonably possible, but also there should be a multiplayer component for both of them to add value. It's the N64 formula that worked well. Go big or go home. 

i believe Bayonetta 2 has been confirm to have co op and go and watch some trailer anasyles for X there is a good chance it might have co op or even be an MMO

Nintendo simply became complacent. Drunk on success. What had happened over the last year or so is thoroughly deserved.

The poor marketing, the slap in the face from 3rd parties, lack of 1st party games with any substance, bad press etc, etc.,

These knocks needed some time to recover from.

It's the going forward from the here and now that will prove Iwata's merit.

And yes, I agree with a lot of what the OP said.