What an interesting thread!
Guy, your observations and recommendations are spot on. The thing is, it all goes back (to borrow a really overused phrase in a geriatric arthritis Rx commercial), to some "simple physics."
Bigger cameras have more mass (which is a bad thing if you have to lug one around all day). But having more mass (i.e. more molecular stuff) it has more inertia (i.e. a tendency to stay put when nudged--a good thing if you want to keep it more still when you press the shutter button).
Smaller cameras have less mass. And that means they can be jostled a bit more easily. So they're more prone to being moving more easily since their inertia is much less. (i.e. they can get rockin' and rollin' with slightest provocation--but they're a lot easier to tote around all day).
But what about the number of megapixels? Well that comes into play here, too. With more megapixels over a given area (FF) you have a greater concentration of them. And with those little photons slamming into a sensor with more tightly packed pixels and photodiodes even the slightest movement could mean a crapload of them will go where you didn't want them to which may result in a 'blur'. (The lens is doing it's thing very precisely but if the camera shifts even slightly...uh oh.) This is, of course, less pronounced with a sensor that's less densely packed like the one in an A7, which is why you'd have a higher success rate with hand held shots at slower shutter speeds. With fewer and relatively larger photo-sites covering the same FF area minute movements won't totally mess up the final image as easily since the Bayer array will allow for a greater notion of perceived sharpness after the 'missing' sites have been interpolated to make up the resultant image file.
Ahh..but what about a camera like the NEX 7? That's got pixels packed almost as densely as the A7r doesn't it? Yeah...more or less. But here we're dealing with a markedly SMALLER sensor and a shutter that doesn't need as much power to travel across the significantly smaller frame to maintain the same exposure time.
That means less energy which means less potential vibration if the shutter mechanism isn't damped enough. Plus, Sony, also made the model have an electronic first curtain so when the image is captured the camera doesn't open then close, it merely closes reducing any additional vibration issues by half. With the A7, the pixel packing isn't as great so slight jostling won't have as pronounced an effect on the final image since the larger pixels and the Bayer array will allow things to be more forgiving. Interestingly enough, with the 15 mp Foveon sensor, since there is NO Bayer array (the architecture is a STACKED set of densely packed photo sites for R, G and B) EACH photo site MATTERS! So you have to be just as careful using a Foveon sensored camera as you would a 36 mp one! As DPx Merrill users (like myself) have discovered, they too have to use good technique, a tripod and 2 sec. self timers to get the most out of their sensors!
There's also another issue. In a FF camera, the shutter has to travel a much greater distance than say an APS-C or MFT camera. While at first blush one might think it's not significant it really is. So you need a solenoid with a greater snap to pull those shutter blades across the frame at speeds that ramp up quickly and stay until the shutter is closed for an even exposure. The loudness that's been reported (and I heard myself in the Sony store) is evidence of that power and transfer of energy to make that happen. And that loud kerchunk you hear is a release of energy which indicates (to me anyway) that there's a lot going on inside the A7r so one had better use good technique to get the most out of that sensor as Guy and others are suggesting.
Solutions?
1. Use a camera with more mass like the D800 or D800e (or a Leica S or MF with a digital back tethered to a computer). And make sure you've got a healthcare plan that covers a ton chiropractor visits.
2. Use as high a shutter speed as you can and a high ISO when holding the smaller FF camera to keep any negative effects to an absolute minimum and use care.
3. Add a bigger lens when you can to the smaller camera to add more mass an increase the inertia to minimize any shaking effects and use care. (By the way, adding the grip will also help keep the inertia at bay.)
4. Use a cable release and use care.
5. Anchor the thing down on a stable tripod and use a care. (Also consider using the self-timer and...STEP AWAY FROM THE CAMERA!)
So if you want to get the most out a sensor with this many photo sites, as has been suggested, you'll have to use very good technique as the higher pixel count sensor can be clearly less forgiving, particularly if you are using it handheld. It's not to say that it can't be used handheld (Vivek Iyer and others have posted some amazing HH shots) it's just that you have to exercise more care and a more deliberate set up in many cases. For many the A7r may not be a walkabout camera like a Leica rangefinder or RX1/RX1r (and the Leica by the way has an amazing amount of mass on board to keep things steady as well as the RX1 and RX1r, which while smaller have significant mass for their size and the shutter, while I'm told is also a focal plane type, seems to be much better damped). It's also why the A7 with its electronic first curtain will may be a better choice for these situations as well.
Of course, if using the A7r means having to shlep around with a tripod and using a more deliberate approach, it kinda defeats the purpose of having the smaller form factor in some cases. So you might as well get the D800/D800e?
But that price is soooooooo sweet.
Decisions...decisions.