I would recommend the Nook HD+. It can be had cheap enough that it's more than worth it. (I have one that's a dedicated xbmc remote/couch surfer/coffee table distraction, as well as another I use as a pdf reader for work.)
If the OP's wife is like a lot of our wives (IE: she's not a nitpicky geek that sits around examining stats with a microscope and spending hours staring at app interfaces -not actually using the app, mind you- just to watch for lag and various other forms of digital navel-lint gazing) and she just wants a full-sized tablet to pick up, web-surf, read, watch media etc. with a decent screen.. then the HD+ will probably be great for her.
The day my wife gives a flying rip about all the minutia that us geeks can fuss endlessly over vs. the above, is the day I fear aliens have taken control of her mind.
1. All Android apps?
There are a few that will show up as "Your device is not compatible" in the Play Store- mainly things that require a camera, GPS or phone hardware that clearly the Nook doesn't have. But as for software you'd generally expect to be able to run, I haven't run across too much that doesn't work.
2. Feature limits: hardware related like lack of cameras. Someone mentioned bluetooth keyboard imitations, but personally, I have no problem using both a Logitech K811, and a Microsoft Wedge BT keyboard with mine. (I'm also running CM 10.2 on both).
IMO, the microSD slot is what puts the Nook firmly above its closest competition. I can understand to some degrees smartphones without an SD slot, but for tablets it just seems silly. Being able to swap in cards full of music/movies, comics, ebooks, etc. for a device that's sole purpose is content consumption is a no-brainer.
3. Stock Android?
As simple as preparing a bootable microSD card (see xda-developers) and replacing the stock ROM with CM10. YMMV, but personally I've nothing but success doing this, and it's made the HD+ feel like a much better tablet.
You can always back up and restore the stock ROM, and you can also test using a hybrid ROM that boots from the SD without touching the stock. I personally feel CM10.1 or CM10.2 are well worthy of replacing stock.
The stock ROM isn't terrible since B&N has allowed the Play Store and third party launchers like Nova. IMO, stock as-is without some level of customizing is unbearable on the HD+, but luckily there's no hacking required to use third party launchers/keyboards, etc.