We don't know what comparisons will be made with our (potential) suggestions. I have a "several year old Canon" HF S100 that does 1080i/p, is small and can take decent stills has an external mic jack, manual audio gain control and fits in a pocket...
4k is still a bit away, though it depends on your definition of "small".
The Sony FDR-AX100 is one of the first consumer-grade "home camcorder" units that does 4K. Not quite as small as you'd like, perhaps, but has been getting good reviews.
There are a few "actions cams" (Panasonic HX-A500, GoPro Hero 4 series, AEE S71 among others). Just because they are action cams does not mean you must strap it on your head - they can be mounted many different ways, including used with a tripod or other common steadying device or (not recommended) handheld.
Some dSLRs that happen to capture video and audio as convenience features are in the Panasonic Lumix DMC-GH4 and FZ1000 - I don't think either will fit in a pocket as the have a "bridge camera" footprint. The Black Magic Pocket Cinema Camera needs a fairly large pocket, too.
Can you define "switch between modes"... what mode switching are you doing?
Editing and storage may be exciting - depending on your environment.
I'm looking for a good HD camcorder that's small, also takes pictures, and turns on quickly.
I have a Canon that's a few years old and the biggest problems are the size and the time it takes to start and switch between modes.
There aren't many reviews on the cnet site and I'm at a loss over where to start looking. I don't want one to strap to my head, just one I can carry in my pocket when traveling that takes good quality videos and pictures.
Are there any 4K home camcorders yet or is that a few years away?

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