Writing rhythms correctly is as important as any other area of writing music. Bottom line, music is read by musicians. Over the centuries music has been noted in a variety of ways. While some of the examples labeled as "incorrect" do appear in classical music scores, we are concerned only with the way music is noted in modern times. Beats are dictated by the time signature.
Middle of the Bar: Musicians like to see where the middle of the bar is. The first example clearly shows where the middle of the bar (beat 3) is in the "Correct" example. The middle of the bar is not so easy to see in the "Incorrect" example.
Half Rests: Half note rests should only appear where they show the middle of the bar. "Correct" shows the middle of the bar (beat 3), "Incorrect" does not.
Complex Rhythms: When writing more complex rhythms, you want to show each beat such as below.
Full Measure Rests: Regardless of the time signature in use, when you have an entire measure with no notes, you always want to use a Whole Measure Rest.