I have a 24-70mm f/2.8L lens and am finding that it is not as sharp as i'd expect. I'm sure it's me and not the lens so hoping someone can help me understand what i'm doing or not doing correctly.
I'm attaching a picture as an example...hand held...here are the settings:
EF24-70mm f/2.8L II USM
59.0mm
1/640 sec; f/2.8; ISO 400
Shutter priority; Spot metering
shot with 70D
when you zoom into the tree it is cleary not in focus/sharp ;(
I've tried at differen shutter speeds but still having the same issue... going to try different apertures next...
Your assumptions are all correct except this one, "Is the 24-70/f2.8 meant to be more of a 'tripod' lens?"
The person that told you that is a moron! 
A piece of glass and it's associated correction lenses get very expensive an difficult to produce as the
aperture gets larger (smaller number). This is why they cost so much more.
For instance a great deal of the 1900-1920 era photographs that are so very sharp were shot at f45. At the time that was as good as it got. Back when I was a kid (mid 1950's) and got my first Argus C3, an f3.5 lens was considered very fast.
Most lenses are very sharp in their center. Stopping down you are using just the center part of the optical elements.
You reduce aberrations and DOF. Pictures look sharper.
A Canon 24-70mm f2.8 is sharper than 90% of all lenses made today. It is so good a lot of photographers are abandoning their primes for it. I have some friends that have no primes any longer at all. It is that good.
So to the point, why is yours not producing very high standards? If you go outdoors on a sunny day, do you get ultra sharp images? Is it just the indoor poorly lighted shots that are fuzzy? Barring you happen to have a faulty copy, very unlikely, I must conclude, it is your technique and just lack of experience.
I stress you try different settings and keep track of what those settings are. What works and what doesn't.
Most of all, keep at it.
The more you shoot and familiar you get with the camera and lens, the better. 
And, be careful from whom you take advise! 
I agree with ebiggs.... no that 24-70 certainly is not a "tripod lens". It doesn't have IS, which is probably what the person was refering to.... but that shouldn't stop you.
You do need to watch your shutter speeds with it, like any lens. Too slow will result in "camera shake blur". But if shooting fidgety kids, you also need to keep the shutter speed up to prevent "subject movment blur", anyway.
Work on your handholding technique. At 24mm you should be able to handhold a sharp shot most of the time around 1/50, at 50mm you might need to use 1/80, and at 70mm you should try to go no slower than 1/120.
The reason to have an f2.8 lens is to have usable f2.8, even if at the cost of some sharpness. An f4 lens will never be able to shoot at f2.8! An f2.8 lens can shoot at f4 or any smaller lens, as well as wide open.
Most lenses improve in sharpness slightly stopped down. With an f2.8 lens, that might mean using f4 whenever possible. With an f4 lens, you'd have to use f5.6 (I do all the time with my 300/4 IS). Or with an f5.6 lens, you might have to use f8 for it to be optimal (with my 28-135 at 135mm, I try to use f8 as much as possible). Or, with an f1.4 lens, it might perform better at f2 (I do that all the time with my 50/1.4).
Still, the 24-70 is better than many lenses wide open. But to improve your odds, you might stop down when you can. Some lenses are optimized for peak performance wide open... I'd consider the 24-70 one of those. The 300/2.8 IS (both version) and 135/2.0 are others.
Often a bigger issue with a larger aperture lens is that focus needs to be more precise. Your depth of field can be pretty shallow - the closer the subject, or the longer the focal length, the shallower DOF will be. Up close to a person for a portrait, focused on their eye, you might find the tip of their nose slightly out of focus!
Here is an example of a very shallow depth of field portrait, shot with a 135mm lens wide open at f2 and very near it's minimum focus distance....
Compare the depth of field about to that in a shot from a bit farther away, with a shorter focal length 50mm lens stopped down a little more to f2.8...
Or this one shot with an 85mm lens from a little farther away, stopped down to f5....
Or this shot from a greater distance with a 135mm lens stopped down to f4....
So you may need to stop down a bit just to get enough depth of field. Or move back from your subject. Or a bit of both.
Also look to your focus technique. For precise focus, you might need to select a single AF point, not rely on the auto selection of AF points (which will focus on whatever is closest, such as the tip of a person's nose, leaving their eyes and especially their ears out of focus when using a large aperture). Search for info about "hyperfocal focusing distance", to have a better idea how depth of field works.
Finally, if you have a filter on the lens, remove it. If you don't already do so, use the lens hood. And, if you shoot a lot of close up, shallow depth of field images and haven't already done so, you may want to fine tune the focus of your particular lens and camera using the Micro Focus Adjustment feature on your 70D.
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7D(x2), 50D(x3), some other cameras, various lenses & accessories
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