Formal:
* The indiscreet release of confidential information led to a major security breach.
* Her indiscreet remarks about her boss quickly spread throughout the office.
Informal:
* My roommate is so indiscreet, she tells everyone about my love life!
* He made an indiscreet comment about the new employee's weight, and everyone was shocked.
Figurative:
* The indiscreet flowers blooming in the garden were a telltale sign of spring.
* The indiscreet whispers of the wind carried secrets across the fields.