That they're able to build a front-end view using the tools the team does. Today, that typically means a framework like angular, react, or vue. That view needs to make at least one api call to a backend & render that data in the view.
That they're able to implement a new method for a backend API. In JavaScript world, this often times involves building or extending an express application with a route. That route should demonstrate the ability to parse a request and shaping the response.
That they're able to model sources of data. Whether that be SQL or NoSQL, you should be able to query databases, create new records, and instantiate new tables or collections.
Skills that make you stand out as a full-stack dev:
Having basic competency across the stack, but an expertise in one-or-more layers
Writing clean code. If your code looks like one long procedural file, I'm not going to hire you. Know how to abstract out code (tDRY) based on responsibility and scale. Bonus points if you've developed the wisdom to know when and when not to abstract.
Writing tests. I'm a firm believer in continuous delivery, and that requires things to be automated. You can't automate delivery if you're manually regression testing. Know not only how to write tests, but how to write code that enables good testing coverage.
RTFM
Good Code Review etiquette
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Minimum full-stack requirements for my teams:
Skills that make you stand out as a full-stack dev: