I've read a lot of posts explaining the ending to Death Note, but they gloss over how Mello realizes the notebook Mikami used was fake. I don't think the anime mentioned it specifically either?
I was confused how Mello came to the conclusion that Kira's henchmen, Mikami, was using a fake notebook, but after reading that and a few other posts, it may have just been his intuition. I think Mello kidnapped Takada betting on the fact that the real notebook will be used to make Takada commit suicide. Since the suspected Kira, Light, and Mikami were being watched, the location of the notebook would be revealed. I might be wrong, but I think if Mikami had a scrap of paper on him like Takada, the team may have never found the second notebook to tamper with.