In case of any errors during sync process Warning Sign will appear next to the sync button on the bottom toolbar. Tapping on it will show some details on what went wrong.
Authorization issues can be solved by signing in again using the same Google Account. Using different Google Account from the one that was used before will replace all tasks in that account in the app, but not in google tasks.
Task Data (title, due date, notes) is different from what is shown in Google Tasks widget in Gmail: try to sync by tapping a sync button on the bottom bar in the app. If sync goes without any issues but the problem still exists, try to modify something in a task and try to sync again.