In 2:12-14 we find Moshe going out from the palace to see the people. He sees an Egyptian man striking a Jew. The passuk says, "ויפן כה וכה וירא כי אין איש....כאשר הרגת את האיש" Moshe turned this way and that, saw there was no person around and he smote the Egyptian... Then he bumps into 2 jews fighting with each other. When he attempts to break up the fight, they ask if he is going to kill them like he killed the Egyptian.
What happened - we know Moshe looked all around to make sure nobody was in sight before he did anything, so how did they know about it?
You can never be sure nobody is looking. If you are going to do something sensitive, unless you are in the privacy of your own home, you have to act with the assumption that somebody might be watching. Even if you look around and take all the protection you possibly can, chances are reasonable that somebody might be watching.
Act accordingly. A person should always be aware that somebody is watching. That somebody might only be Hashem, and you should act appropriately, but even if you are doing nothing wrong, that somebody watching might be not just Hashem but someone human as well.