(From left to right and top to bottom; top of lens barrel, bottom of lens barrel; left hand side, right hand side; front and rear.)

As we'd expect from a Canon L series lens, build quality is exemplary, with top quality materials and finish. This is precision mechanical engineering in a form rarely seen in photographic equipment today, and a far cry from the all-electronic buttons and dials found on modern DSLRs. All controls and movements are beautifully smooth and precise, and for a lens offering such flexibility of movements, it's remarkably straightforward to use.

The controls for the various movements are arranged around the faces of the barrel in a fashion that simply begs use of the word 'festooned'. In the default configuration as shown above (with no rotations applied) the tilt controls are at the top and bottom of the lens, and the shift controls on the two sides. Two small lever tabs on the right hand side (i.e. beside the camera's handgrip) unlock the independent rotation movements for the tilt and shift axes. These levers are rather small, and may not endear themselves to landscape photographers who need to wear gloves. Overall though, it's an incredibly well thought out design, intuitive and with few operational quirks.

On the camera

The TS-E 24mm F3.5 L II is a fairly big, chunky lens, and is notably larger than its predecessor. The new barrel design results in an 11mm (0.5") increase in diameter and a 19mm (0.75") increase in length, with weight going up substantially too. This makes the new optic similar in size and weight to many of Canon's familiar L series lenses (similar in diameter to the 24-70mm F2.8 and 24mm F1.4 L II, and about halfway between the two in length). Like Canon's other TS-E lenses (and the reason why they don't qualify for the usual 'EF' designation), the 24mm F3.5 L II is manual focus only.

Lens body elements

The lens uses Canon’s all-electronic EF mount, and will fit all of their DSLRs regardless of sensor format (APS-C, APS-H or 35mm full-frame). There's no O-ring weather seal around the lens mount - weather sealing such a complex device is never going to be a realistic option.
The filter thread is 82mm, as used on the 16-35mm F2.8 L II. The rear-focus design means that the front element does not rotate on focusing.
The bayonet mount EW-88B hood comes as standard, and can be reversed for storage. The interior is lined with black felt to minimize reflection of stray light into the lens.

This bowl-shaped hood is shallow (just 19mm deep) but very wide in diameter (12cm). It's not easy to accommodate in a bag; and Canon also recommends a using piece of card to further shade the lens in bright conditions.
The focus ring has a 24mm wide ribbed-rubber grip. It rotates approximately 100 degrees from infinity to the closest focus of 0.21m, with a beautifully smooth and precise action. The angle of view noticeably decreases on focusing closer.
On the top of the lens barrel is a large knob controlling the tilt movement. This offers 8.5° tilt either side of centre, with a scale marked at 1° increments. There's a firm detent at the neutral position.

Note that while the older TSE 24mm had the extremes of the scale marked in red to indicate a risk of vignetting, that's not the case here - a benefit of the larger image circle.
On the base of the lens we have a small knob for locking the tilt movement at the selected position, plus a second switch which can lock the tilt movement at the neutral position only. This may look like it's redundant, but is actually a very welcome addition as it stops you from accidentally tilting the lens either when taking it out of the bag, or when shooting handheld. There's also a duplicate tilt scale.
On the left side of the lens (looking from the rear) is a medium-sized knob controlling the shift mechanism. This offers ±12mm movement, with a scale marked in 1mm increments (and once more with no red marks - all positions are accessible without significant vignetting). Again there's a firm detent at the central position.
Also included is this larger add-on knob for the shift control, which is recommended for use on cameras which don't have a built-in flash. It's easy enough to install, just as long as you've got a small enough screwdriver.

It's well worth using if you're shooting 1D or 5D series cameras, as it makes the shift control more precise. However as you can see here, it does block visibility of the shift scale.
On the right side of the lens beside the camera's handgrip there's a small locking knob for the shift movement, plus a duplicate shift scale. The two small lever tabs release the rotation movements by pushing backwards towards the camera body. The one at the rear of the lens is for rotating the shift mechanism, and the more forward of the two for the tilt.
Here's the tilt movement set one extreme position, of 8.5° to the left.
This is the lens set to maximum shift, of 12mm upwards.
The tilt movement rotates 90°, with a detent at 45°. The locking lever engages at the two extreme positions.
The shift movement rotates 180° (±90° from the central position), with detents at 30° intervals. The locking lever engages in the central and two extreme positions.
This array of tilt and shift movements and rotations gives rise to an extraordinary degree of flexibility, that was once the sole preserve of specialist large format systems. Here the shift movement is rotated 90 degrees, and set fully to the right; the tilt movement is then rotated 45 degrees and set fully towards the upper left.
With such a plethora of controls and movements the occasional conflict can inevitably occur. On an APS-C body (here the 50D) with the shift axis rotated 90 degrees, the shift control knob gets hidden under the flash housing.

In this example, that inaccessibility is compounded by rotating the tilt axis back again, which further blocks the small shift control knob with the larger one for tilt.
One other conflict that can occur is again with the shift axis rotated 90°. Adding full shift to the right results in the shift rotation lock lever becoming hidden under the barrel.

To be fair, in actual use this is unlikely to be a significant problem; just shift the lens back before rotating it again.

Reported aperture vs focal length

This lens allows an aperture range from F3.5 to F22 to be selected.