Ya I really don't understand why he didn't ask Anakin to join him in arresting Palps. Anakin fully regained his trust by ratting out palps. Anakin was the first to figure out who he was, and he turned him in without even thinking. So...
1) If Mace believes that Anakin really is the Chosen one, he should allow Anakin to fulfill his destiny and go with him to get palps.
2) If Mace thinks the chosen one thing is bullshit, he STILL should take Anakin with him, because Anakin is one of the strongest Jedi they have.
Either way, Mace should have asked him to go. I think he wanted the credit for killing him, and it cost him and thousands of Jedi's their lives. If Mace just gave his ego a rest, and took 10 powerful Jedi's instead of 3 Tools with him, this would all have gone differently.