If I remember Nimoy's book right, Shatner pranked him with the Dobermans bit, and while Nimoy was a bit annoyed by it, he didn't hate Shatner for it.
Shatner, even by his own admission, was an egomaniac, and while Nimoy and he were generally friends and Nimoy could look past it, most of the other cast members really didn't like him.
Nichelle Nichols rarely agreed with the guy (except for screwing up the kiss scene in that one episode so they'd have to film a black woman kissing a white guy, they agreed to make the TV execs film that for syndication even if they had to bungle every take that tried to cut away to force them to), and they eventually mended fences.
James Doohan really didn't like Shatner while liking the character he played due to the ego thing, but they eventually mended fences too, shortly before Doohan had Alzheimer's, fortunately.
Most of the other cast had similar relations with Shatner, all eventually letting bygones be bygones save George Takei, who Shatner tried to make amends with at one point, but Takei apparently wouldn't reciprocate.