Be a sign of the times = something that shows that society now is worse than it was in the past. ( a typical thing about the time we live in)

• These riots are a sign of the times.
• The fact that he had been dead for a week in his apartment before anybody found him is a sign of the times.
• It’s a sign of the times that you cannot speak to a real human being when you telephone a bank.  All you get is an automatic voice,

At the end of the day = ultimately, eventually, in the final analysis;  when everything is taken into consideration.

• At the end of the day I’m responsible for what happens in the school.
• Of course I will listen to what she has to say but at the end of the day, it’s my decision.
• At the end of the day it is up to the management to decide.

Out of date = old and not useful.

• My computer is out of date.
• This milk is out of date.  I will throw it away.
• Many of the facts in the book are now out of date.
• Out of date technology.