Learn Danish: Vores by har mindst arbejdsløshed. - Our city has the least unemployment.

Mindst is the superlative form of lidt (a little). It is used for uncountable quantities, like arbejdsløshed (unemployment) or time. If you were talking about countable things, like having the fewest unemployed people (færrest arbejdsløse), you would use færrest.

Why isn't there a definite article like den mindste arbejdsløshed, since the English translation says 'the least'?

When superlatives of quantity like mindst (least) or mest (most) are used directly before an abstract or uncountable noun to simply measure amount, Danish drops the definite article. It behaves purely as a quantifier telling us 'how much' rather than an adjective describing a specific physical object.

How is the long word arbejdsløshed built?

It is a compound word made of three distinct parts that are very useful to learn. Arbejde means work, -løs is a suffix meaning without (like the English -less), and -hed is a noun-forming suffix just like English -ness. Put together, it literally means work-less-ness.

By is a common gender noun (en by). Does vores change if we use a neuter noun instead?

No, and that makes vores one of the easiest possessive pronouns to use! In modern everyday Danish, vores stays exactly the same whether the following noun is common gender, neuter, or plural.