Exposure, well, if you're using green-box Auto, that's a risk you take, but if you're spot metering, as well as spot AF, chances could be you didn't aim where you thought you aimed.
The lack of IS could be another issue, if you were used to having it on the 18-135. Increasing your shutter speed to at least 1/focal_length is a given, and you may want to consider doubling that, if you don't have good handholding technique. The additional weight of the 24-70L may be something that's throwing you off if you've still got the newb cupped left-hand around the side of the lens hold, rather than a proper SLR grip, with your left hand, palm up, beneath the lens/body, forefinger and thumb wrapped around the lens. Timing your breathing, watching your posture, elbows, and feet are all part of good handholding technique. Tripods are great, too.
Suggest you test in good light, on a tripod, at a perpendicular target, with manual focus to see if your lens has issues. It's highly unlikely, but possible. What you'd look for would be an image softer on one side than the other (decentered element), or other huge issue. If that checks out, then you need to consider autofocus technique, settings, and calibration.
The reason the Canon prosumer bodies have the ability to do autofocus microadjustment is that lenses and bodies can be out of calibration to each other. While each is calibrated to a specification at the factory, there is an acceptable margin of error. So your body might be +2, and your lens might be -2, and when you put them together, you get a difference of 4, which is then noticeable and not acceptable. Consider learning how to calibrate your camera/lens combination.
Also, L lenses, particularly first L lenses, nearly always come with a helping of buy's remorse because of the pricetag, and because you've mentally built it up into this perfect thing: perfectly sharp, perfectly beautiful, perfectly whatever. It's not. It's still a lens. It's still made of glass that obeys the laws of optics. You have partially paid for performance you can't use (full-frame corner coverage); and you've paid for heavier build quality, and a larger max. aperture.
But Ls aren't necessarily better than their EF-S counterparts, which have several design advantages from the smaller image circle they project. Just because EF-S lenses aren't Ls doesn't mean they're not as sharp--or sharper--remember, too, some of the Ls are film-era design, while all the EF-S lenses are digital-era. Consider, too, that 24mm is basically 35e on a crop body, and that you can't really use this lens for wide-angle shooting. This can all add up to a heaping helping of buyer's remorse, and could make an EF-S 17-55/2.8 more attractive if you aren't planning on moving to full frame in the near future.
Just a thought.