Things about Purim that bother me
In no particular order

1) The Persian sources are't especially gap-filled yet they contain no references to the events described in Megilas Esther. There's no record of a King Ahashverosh, a Queen Vashti, a decreee to kill Jews, or of Jews killing thousands of their enemies. Why wasn't any of this recorded?

2) The names Haman, Esther and Mordecai sound suspiciously like those of Babylonian gods, making it possible that our story is a retelling, maybe a parody, of some ancient folktale or myth. In Persian mythology Ishtar is the goddess of fertility; Marduk is the chief guardian of the heavens; and Haman is the underworld devil. Is this a strange coincidance? A deliberate parody? Or (more) proof that the whole "lo shanu et shimon/they didn't change their names" is just so much Haredi bushwah?

3) Esther is a Jewish woman, living well after the Torah was given. So what is she doing in a harem, paying no attention to dietary laws? And, is anyone else concerned that Mordechai seems to have been the original funny-uncle?

4) Late in the story, a guy named Hatach appears. Essentially, he's Esther's messanger-boy, yet the Rabbis insisted he was the very famous Daniel. Why is this necessary?

5) Early in the story, the King receives advice from a man named Me'muchan. The Rabbis insist that this is Haman. Why is this necessary?

6) The Rabbis also insisted the Vashti had a tail. WITN?

7) Hasidim, who are otherwise perfect in every way, and the apogee of authentic Judaism, make a fetish of mispronouncing Mordechai's name. Instead of Mor-DOH- Chai, they say Mud-cha. WITN?

A question I can answer: In the Megillah, Esther three-day fast is long before Purim, so why is Ta'anit Esther, the rabbinic fast day, on 13 Adar, the day before Purim?

Short Answer:
The Rabbis were shrewd at politics.

Long Answer:
Second Temple Jews had a holiday that the Rabbi's disliked, called Nicanor Day, which commemorated a major Maccabean victory over a Greek general named Nicanor. Nicanor Day was celebrated on 13 Adar. The Rabbis, who disliked Macabees, turned Nicanor Day into a solemn fast day. (Four legs good! Two legs better!)