Line-breaks and paragraphs in comments are not supported. The shift-enter is intended only to affect the situation while you edit.
It is possible to work around this restriction via using MathJax. But doinng so is discouraged. If you need some visual separation, use some symbols for example // like this:
This is one important remark I want to make and this will take up a couple of lines. Maybe two or maybe three. It is really interesting and deserves to be elaborated on. // This is another important remark that is unrelated. It is really interesting and deserves to be elaborated on.
Also, posting two comments instead of one, can be a good option. Especially when the two ideas are quite unrelated.
For posts (question and answer) this is different:
You can start a new paragraph by leaving at least one line blank. Leaving more than one has no additional effect though.
You can start a new line by leaving at least two spaces at the end of a line. Like this.
Here a new line.