It's never explained how Kahless knew about Worf's childhood vision. It would have to have been inserted into Kahless's memories by the high priests. That means that Worf must have shared his vision with others, which explains why Kahless's knowledge of Worf's intimate thoughts wasn't enough to convince Worf of his authenticity.
It's pointed out that Worf's word goes far in Klingon society. This was apparently why the high priests chose him to be the one to whom Kahless appears. But Worf was there for ten days and almost left before Kahless appeared. Koroth even had to show up personally to convince Worf to stay. Later, Kahless reveals knowledge of a specific religious experience that Worf had. We learn even later that all of Kahless's memories were inserted by the high priests. Taken altogether, it seems as though the high priests were scrambling to insert Worf-specific memories into their sleeping clone in time for him to appear before Worf, and the high priests almost missed out.
Some have suggested that the Idiot Ball applies when nobody suggests "clone" as an explanation for Kahless's presence until that fact is revealed. However, this may be justified since Kahless's reputation is so great that the relevant parties believe that anyone with access to Kahless's DNA, such as the Klingon priests, wouldn't use it to create a clone in the first place. Nobody was being "stupid"; they just didn't consider how someone loyal to Kahless's example could justify cloning him in the first place.
