Body & Design
The D610 is essentially the same as the D600 from a physical point of view and, for that matter, pretty consistent with Nikon's other DSLRs. Both cameras have much in common with the D7100, and share most of its button layout. In common with the enthusiast-focused D7100, the D610 has a lockable exposure mode dial with a lockable drive mode dial underneath it. The only difference is the position of the magnification buttons, which are shifted downwards one position.
Other than that, it's a pretty standard Nikon arrangement, with a movie/stills switch around the live view button and the combined AF/MF switch and AF mode button that have swept across the company's DSLR range. It's a fairly well-polished arrangement, giving lots of buttons for direct access to features such as white balance and ISO. The latter isn't especially well-positioned for using with the camera to your eye, especially with larger lenses, but this is largely made up for by Nikon's excellent implementation of Auto ISO.
The D610 continues to offer the eight-way controller that positions the AF point in manual selection mode - it's an important part of the Nikon control system and is necessary for making use of the camera's 39-point AF system. This can be locked to prevent accidental use, if necessary.
In your hand
The D610's handling is exactly like that of the D600. It's not a small camera by any means, but it's less of a lump than the D800. In fact it's not that much larger than the D7100, underlining its position as the enthusiast-level full frame model.
While the inner frame of the D610 is magnesium alloy, there's quite a bit of plastic on the outer shell. That's less of an issue on something like the D7100, but on a $2000 camera, you'd expect metal on the outside, as well.
Like the D600, the D610's optical viewfinder is very large, and the same size of the more-expensive D800. A large viewfinder is one of the big reasons for moving up to a full-frame DSLR. The magnification is 0.70x and the coverage is 100%. The similarly priced Canon EOS 6D's viewfinder is a close competitor, but its coverage is a slightly less-impressive 97%.