Several hints in Megillat Esther imply that the sin of Am Yisrael is the abandonment of the mission of returning to Eretz Yisrael and rebuilding the Beit HaMikdash:
Parallels between Ahashverosh's Palace and the Beit HaMikdash
The use of the term "Birah" - a term used only for the Beit HaMikdash and Shushan
70 days between Haman's letters of destruction and Mordekhai's letters of salvation are reminiscent of the 70 years of exile