I don't see Nintendo going third party any time soon. However, if they do make another console and it flops like the WiiU is doing, then they'd best abandon the console market and go solely with handhelds. I love my Vita and play it more than anything else at the moment simply because it's so convenient, but I can't deny that the 3DS is blowing it out of the water when it comes to sales. There are also a number of properties that the 3DS has that aren't available elsewhere (Phoenix Wright, Professor Layton, Fire Emblem, new Shin Megami Tensei) that if Nintendo can keep hold of, in addition to their normal first party titles, will keep them in the lead on handhelds for a long time.
A lot of money goes into the R&D of a new console, and Nintendo has lost pretty much all of it on the WiiU since no one is buying it. I agree they need to continue supporting it as best they can or they will lose any consumer trust they still have. Meanwhile, if they plan to stay in the console business, they need to spend a lot of that money on the features that people want. They need a good network infrastructure for online play. They need a main user account that will have access to all purchases made on their stores that works across all their devices. They need to include a Blu-Ray player so people can watch their movies without needing a dedicated player in the living room (though really, this point may not matter for the next console, as it seems lots of people are moving away from physical media).
If they make some kind of special peripheral like the WiiU's GamePad, it should be optional, rather than coming with every device, unless it has an obvious benefit or use that every developer will want to incorporate. Right now, the GamePad is almost completely under-utilized except maybe for remote play. I have not seen a single game that uses the GamePad in a way that couldn't be done just as easily with an onscreen menu and it doesn't appear that any game in the pipe is focusing on using the Pad in an innovative way. As such, I believe the GamePad is a large part of the failure of the WiiU (in addition to poor advertising and lack of high demand titles), as it upped the cost of the console package considerably.
Finally, they need good titles ready to launch with the platform and excellent titles to follow every three months or so for at least a year. Not just their usual lineup either, but some new IP mixed in. Launch with a Mario Bros. and a couple of new IP's. Three months later, release more new IP games and Zelda. Three months later, Mario Kart. Round out the year with a new Smash Bros. In between you can have smaller titles like Pikmin, Luigi's Mansion, Paper Mario, etc. Plus, make it so the third party developers WANT to put games on your console. Cut them an amazing deal on licensing for the first year or something, but make sure those 3rd party games are available.
The WiiU did NOTHING with it's first party content. There's actually a good number of third party releases on the platform when you look, but they were almost all games that also came out on PS3/360 which people already had, many of which had been released MONTHS earlier on the other systems. The other exclusive titles were of the usual launch title quality. Nintendo needed to push their exclusives right away, and while they started okay, they didn't do it enough. They had New Super Mario Bros U and NintendoLand, which are still the top two selling games for the platform and that's it. Next big releases were 7 months later with New Luigi U and Pikmin 3!! Those should have been out in Feb-Mar 2013. Next big release was a Zelda remake in October and finally a real big seller with Super Mario 3D Land a full year after the console launched.
I'm not going to consider a Zelda HD remake as a highly anticipated title. In fact, the only game on that list that I consider highly anticipated is 3D Land, which is probably why it's the third best selling game for the WiiU, despite being one of the newest. They should have had one highly anticipated title out every three months. Instead it took a full year for one. I think the only anticipated title that even has a release date is the next Mario Kart. Even Bayonetta 2, which was a huge part of their initial advertising since it's going to be exclusive to the WiiU doesn't yet have a release date. All we have been told as far as Bayonetta and Smash Bros is 2014. Some future Zelda game? Metroid? Kirby? Kid Icarus? All their other titles? Nothing. Either no release date or no plan to make a game for it. They have a ton of unused IP that's molding in a closet somewhere that should have been helping to sell their platform.
God, after typing all that out, I'm just downright disgusted with Nintendo... They aren't even trying because they didn't think they'd need to after the success of the Wii. Well wake up! No one who picked up a Wii because of the innovative motion control cares to purchase a new console. They had their fill of it and don't see the need for a new console that does the same thing. Wii's were purchased by retirement homes and hospitals and even enterprise-scale businesses as it gave people an opportunity to come together and goof around while getting some exercise. They still have these systems and don't need to replace them. The lighting that was the Wii is not going to strike twice.