1. We have to make this written proposal the best one they receive. We have to make sure we dot the i’s and cross the t’s.
2. I was in a hurry to get this letter to the lawyer. It was more important to get it mailed today than to dot the i’s and cross the t’s

The expression probably originates from the idea of being careful to complete the letters “i” and “t” in cursive handwriting to ensure they are clearly identifiable from each other.