I have an idea about a code-golf challenge.
Will I need to verify/test every answer submitted ?
Will I need to run code submitted to be sure that the answer meets the requirements ?
But what about the rest? Focus on the most important answers. If you are planning to accept an answer make sure that it meets the spec by testing it. That normally means you just need to test the shortest submission — and if that turns out to be invalid, move on to the next shortest. In case you're unable to test the currently leading submission, you can still rely on the community to test it for you. E.g. you could pop into chat and ask whether someone would be able to test the code in question. Usually someone will be able to run the language. (Unless it's TinyMUSH...)
In addition to the answer you want to accept, you (and ideally everyone else) should make sure any answer works before even upvoting it. (Unfortunately, this is far from reality... I've seen answers get a bronze badge before anyone noticed it didn't meet the spec.)
For code golf, you don't have to verify the answers yourself. Verifying all of them personally could be time-consuming or downright unfeasible (after all, not all languages are free and run on all platforms), so you can rely on the community to do this for you.
This will become a lot easier if:
The question has a clearly established validity criterion.
The question has test cases.
It is generally expected that the original poster (OP) will make a final decision in some corner cases. For this purpose, other users generally post comments like This answer does X but the question says Y. Is that allowed? and await a ruling from the OP.