There are 3 main symptoms of a bad thermostat:
It may run all the time, causing the temperatures to get too cold.
It can shut off too soon, causing warmer temperatures then desired or needed.
The switch contacts can stick open, not allowing the unit to run. Sometimes by turning the thermostat all the way off and back on again, will free the contacts.
These are the 3 main symptoms of a bad thermostat. I hope this helps you. If you need more assistance, you can resubmit your question with more details.