Because physics describes reality, your solutions to any physics problems you tackle should be able to describe reality, too. You can avoid many mistakes by checking that your answers have the following properties:
They have the right units. If a problem asks you to find a speed and you get 5 kilograms, you know you made a mistake somewhere. (Note that this check only works if you keep track of your units throughout the whole problem.)
They’re the right size. If you calculate that the mass of a planet is 53 grams, that the speed of a soccer ball is 3 trillion meters per second, or that the temperature of ice is 350 degrees Celsius, start searching for the mistake.
They point in the right direction. When you’re looking for a vector, sometimes you know roughly what direction it should point.
They have the right sign. If you find that the density of a liquid is –1,200 kilograms per cubic meter, you made a sign error along the way.