i've always believed that it has something to do with Dana's mental problems. becoming a Slayer affected her in ways that differed from the others. she had vivid dreams about the deaths of each Slayer before her, to the point where she confused the lives of past Slayers with her own past, believing that Spike was the one who killed her family and kept her locked up for God knows how long. but what she was remembering was the last moments of the Slayers Spike killed...the Chinese girl in the Boxer Rebellion, and Nikki.
all Slayers are capable of what Dana did. being trained isn't what gives a Slayer her strenght. the strength comes from being Chosen. the training only helps in harnassing that power, working it into an asset, a weapon, instead of uncontrolable power.