When hate pulled Doohan and rest of the B-team by the nose (where Shatner was concerned), there would be no chance to settle matters.
However, the report that I have heard from multiple sources is that Doohan and Shatner did finally manage to patch things up sometime before Doohan's death. Shatner says he began to make some attempts to repair some previously burned bridges while they were shooting Generations, and I believe both Shatner and Doohan's widow have said that they patched things up between them prior to his death.
There may very well have been some legitimate issues between Shatner and other cast members at the time of the original series. However, based on everything I have read, my gut tells me that they were not nearly as serious as made out to be. And I get the distinct feeling that as far as Shatner is concerned, all of that is ancient history. But some of his co-stars, Takei in particular, have made it part of their careers to bash Shatner, and seem uninterested in burying the hatchet, so to speak.