So this has been reviewed time and time again on the internet, but here's my short take on this one.
1. Beautiful photos and videos. Full frame, 24 megapixel sensor that has fantastic high ISO performance. Bokeh like mad. Natural cinematic look. Absolutely no other DSLR will take better photos than this camera, no matter how much higher of resolution they have. They may equal or surpass on things that are basically overkill (like high megapixel sensors, faster burstrates, or autofocus) but the photos that come out of this are no worse than any other full frame camera on the market.
2. Yeah, that whole 'oil on the sensor' thing... apparently many people have had issues with this. I on the other hand, have not had this issue come into play - and it's even less of an issue if you have a camera store that does pro sensor cleaning - Nikon will hook you up with a sensor clean for free.
3. Video is fantastic. Just as good as the 5D series from Canon, and possibly better, being that it has a mic/headphone jack, onboard audio monitoring, and a dual SD card slot... It works great. There is the nuance that you can't change your aperture in live view when using your brand new G-lenses that don't have aperture rings, but this isn't even a problem if you, like me, are fine with using the D-series lenses or manual-focus vintage lenses from the AI/AIS days.
4. Viewfinder is pretty, clean, bright, and big. Easy to compose with.
AF is fast and accurate. Though the 39 AF points are centered around the middle, not a single other camera I've used has a much better AF sensor array that covers a particularly larger area... Besides, I learned to focus and compose independently anyway as to assure myself that my subject is in focus, so this is absolutely fine.
5. Battery life is fantastic, even in video. All-day shooting on 3 batteries is totally feesable if you're not leaving the live view on constantly... if you are, then 4 batteries is all you'd need for 8 or so hours of shooting.
Overall, this is a fantastic full frame camera, and even though there's the whole issue with oil on the sensor, it's almost worth it now that you can get these for under a grand... IF you don't trust it, and want a camera with better video options and don't mind having a more plasticy camera, the D750 would be the way to go, as it has just a few more features in whats basically the same body.