[EDIT]
This answer has been edited. I’m leaving the original answer below for context (otherwise the comments wouldn’t make sense).
When this question was originally asked, JSLint was the main linting tool for JavaScript. JSHint was a new fork of JSLint, but had not yet diverged much from the original.
Since then, JSLint has remained pretty much static, while JSHint has changed a great deal – it has thrown away many of JSLint’s more antagonistic rules, has added a whole load of new rules, and has generally become more flexible. Also, another tool ESLint is now available, which is even more flexible and has more rule options.
In my original answer, I said that you should not force yourself to stick to JSLint’s rules; as long as you understood why it was throwing a warning, you could make a judgement for yourself about whether to change the code to resolve the warning or not.
With the ultra-strict ruleset of JSLint from 2011, this was reasonable advice — I’ve seen very few JavaScript codesets that could pass a JSLint test. However with the more pragmatic rules available in today’s JSHint and ESLint tools, it is a much more realistic proposition to try to get your code passing through them with zero warnings.
There may still occasionally be cases where a linter will complain about something that you’ve done intentionally — for example, you know that you should always use === but just this one time you have a good reason to use ==. But even then, with ESLint you have the option to specify eslint-disable around the line in question so you can still have a passing lint test with zero warnings, with the rest of your code obeying the rule. (just don’t do that kind of thing too often!)
[ORIGINAL ANSWER FOLLOWS]
By all means use JSLint. But don’t get hung up on the results and on fixing everything that it warns about. It will help you improve your code, and it will help you find potential bugs, but not everything that JSLint complains about turns out to be a real problem, so don’t feel like you have to complete the process with zero warnings.
Pretty much any Javascript code with any significant length or complexity will produce warnings in JSLint, no matter how well written it is. If you don’t believe me, try running some popular libraries like JQuery through it.
Some JSLint warnings are more valuable than others: learn which ones to watch out for, and which ones are less important. Every warning should be considered, but don’t feel obliged to fix your code to clear any given warning; it’s perfectly okay to look at the code and decide you’re happy with it; there are times when things that JSlint doesn’t like are actually the right thing to do.