I've got ready access to the FZ1000 and have used it a few times. My take:
There are a lot of things to like - 4k, decent lens etc. Image stabilisation is superb. I never normally use autofocus, but the face detection on the FZ1000 was so good I ended up letting it do the legwork on that front with no errors at all. There are some drawbacks I've discovered for shooting video though:
1 - using the wifi link seems nice as your iPad turns into a director's monitor very easily BUT the screen on the camera switches off after 30 seconds of recording when wi-fi is on, so you end up having to use the iPad / phone to monitor - also, the iPad will display everything on the screen except the audio levels for some reason, so a fail on that front.
2 - Using a monitor via the HDMI works very well until you hit record and the monitor feed switches off (like the 5D used to), so no good there. However you can have a clean feed, so I think this camera would work very well with a ninja or similar.
3 - No headphone jack. Why??? Another reason to use a ninja.
4- I shot on Cinelike D and found it to be more noisy than I'd hoped. Not terrible, but not great. Back to Cinelike V for me.
5 - No ND as Andrew says - you could use vari NDs, but I'm not a fan of them as you have to unscrew them to get clear. I use Cokin adaptors, which work brilliantly with the FZ1000's fixed lens as you can leave the adaptor on the whole time, which allows you to drop in filters within 5 seconds and of course gives you lots of options for polarisers, grad NDs etc (and also gives you a little bit of flare protection).
6 - 1" sensor takes me back to old school ENG shooting a bit - it's harder to get shallow DoF but it can be done if you frame at the right focal length and separate your subject, etc. That lens gets to F4 fairly quickly (around the 50mm mark if memory serves) so you'll never use it as your primary shot, but it's fantastic as a wide angle 2nd cam on an interview for instance.
All in all I'd say this is a really good semi-pro camera that can be used to get away with pro shoots if speed and simplicity are needed, but don't rig it up like other DSLRs - this is a camera that works best on it's own. I'll definitely pull it out for handheld GVs and the occasional vox pop.