More than anything else, Candy just wants to be useful to other people. His age and disability act as a constant reminder of how he's been discarded by society. He needs a place in life where he can make some mark upon the world. It's not surprising, then, that Candy jumps at the chance to buy into George and Lennie's dream of owning their own farm. So his attitude towards George and Lennie is generally positive.
The same can't be said in relation to Carlson. When Carlson proposes that Candy shoot his dog, it brings home to him how increasingly useless he's becoming on the ranch. In the pathetic figure of his decrepit old dog, Candy gets a chilling foretaste of his own fate.
Candy also doesn't have much time for Curley's wife, but then no one does, really. But in his case he has a particular reason for not liking her. Her overpowering sexuality constantly reminds Candy that, as he's severely disabled, he's considered something less than a man. Curley's wife also cruelly taunts him, mocking Candy as one of the "weak ones" no longer permitted to visit the brothel.