JSLint tests a professional subset of Javascript, created by Douglas Crockford. Essentially, he seeks to carve only the "good parts" out of the JavaScript language, to make life for programmers easier and code more legible and predictable. So, the short answer is NO. You do not have to follow the instructions. Perfectly valid JavaScript code will, and does, fail JSLint all the time.
But the long answer is that your life will be significantly easier in the long run if you do.
Take === vs. ==, for example. The difference is testing for EQUALITY versus testing for IDENTITY. Or, as Crockford says in his book, JavaScript: The Good Parts:
JavaScript has two sets of equality operators: === and !==, and their evil twins == and !=. The good ones work the way you would expect. If the two operands are the same type and have the same value, then === produces true and !== produces false. The evil twins do the right thing when the operands are of the same type, but if they are of different types, they attempt to coerce the values. The rules by which they do that are complicated and unmemorable.
So, if you're using === instead of ==, your code will almost always perform as you expect it to, a small price to pay for typing an extra character. But if you use == and the operands are not of the same type -- a string and an integer, for instance, JavaScript will first translate those values to the same type, and then compare them. And they might not do what you want or what you expected. And since, in JavaScript, you're often dealing with elements brought in from the DOM, which come in as strings, you run into string conversion issues all the time.
As Crockford writes, here are some of the issues you could run into:
'' == '0' => false
0 == '' => true
0 == '0' => true
false == 'false' => false
false == '0' => true
Screwy, eh? JavaScript: The Good Parts is a great book, super thin, and if you've been working with JavaScript for a while, it will change the way you code for the better. So will JSLint, if you bow your head like a good marine.
So. Long answer? No. You don't have to do everything JSLint tells you. But you should.