Got one of these cameras for my birthday and took it and used it almost exclusively on holiday.
First thoughts, with more to follow after I have been through more of the pictures I took.
It is very small, so easily pocketable. It is so far jolly rugged. I used it in the sea and in the pool with no problems, although I did not go more than a few metres deep in either medium. The controls are pretty basic. There is an 'A' mode, but only offers a very limited choice of apertures at any given focal length. With a sensor this size there really isn't much point. There are no manual or shutter priority modes.
The WiFi means that at the end of the day pictures can easily be transferred to a tablet, or in my case a phone. Although it seems that only jpgs are transmitted, of which more later. The 'phone app that is used with the camera also permits live view remote control.
Start up time is very quick, as is focussing after the shutter release is pressed half way. AE is locked with the button halfway down, and the focus can be manually adjusted afterwards if you are so inclined. It is not a 'super zoom' camera, just having 4x optical zoom which I don't find an issue, although others might. There is a digital zoom function tacked on the end of the optical range. My opinion of digital zooms is not for sharing in polite company . . .
Like all the compacts I have used noise is a problem, but this is definitely the worst: apparent at even the lowest ISO rating of 100 if the light is not super bright. Which might help to explain the harsh NR applied to all jpgs. Effectively the jpgs, even on 'fine' from the TG-4 are usable for social media, but really nothing else, as they are seriously over-sharpened, smeared and full of jpg artefacts. So it is jolly good job that the TG-4 has RAW. It is not possible to shoot RAW only, the selection is RAW+jpg, which not only wastes card space, but enables direct comparison between the rather noisy but fixable RAW images and the IMO awful jpgs processed at the same time.
Battery life is exemplary - my Fuji X20 would have had to be charged at least 3 times compared to the Olympus once, and even then that was a precautionary charge as I don't yet how accurate the battery meter is.
I took a few underwater videos, but I have only looked at the resulting footage on the camera screen so far.
Overall impression is that this is a flawed but really useful and fun travelling companion. I especially liked the underwater performance. I shall post some pictures from it in due course.