I have bought and sold five of the 24-70mm L lenses, none could match my 24-105L. Many used ones on the market need repair, they are easily decentered and the guide bushings that support the telescoping part of the lens break and jam and then the lens stops focusing accurately.
If you get one, plan on sending it to be repaired, since many selling used ones don't recognize the subtle problems, they just know that they want something better. This means allowing $350 or so in the price you pay. Obviously, if the lens has just returned from a Canon servicing, that would be better, but I'd then wonder if Canon was unable to put it into the condition that the owner expected, so he is dumping it.
The worst MK II is better than the best MK I in lens rental testing, and they are better constructed. Thats something to consider.
Also note that the IQ of the Tamron 24-70 IS is better than the Canon MK I, so for the price, I'd prefer it.
For walking around in fair to good light, its hard to beat a 24-105mmL. Again, there are good and bad, so if buying used do not accept lens creep, and plan on a trip to Canon for checkout and repair. New 24-105mm L's from kits can be found for under $800, I paid $700 locally a few years back.