The Inspector would be a useful tool for which of the following tasks?

The Inspector is a powerful tool built into web browsers that allows developers and designers to examine and manipulate web page elements in real time. It provides insight into the structure of a webpage, including its HTML and CSS. When it comes to testing small CSS changes, the Inspector shines by enabling users to quickly try out different styles without permanently altering the code. This instant feedback loop helps designers see the effects of their changes immediately, making it a vital tool for fine-tuning the look and feel of a website.

The other choices involve tasks that are not primarily within the scope of what the Inspector is designed for. Fixing server errors typically requires access to server-side code or logs, adjusting browser settings is done through the browser's settings menu, and writing HTML code is best accomplished in a text editor rather than within the Inspector itself. This reinforces why testing CSS changes directly through the Inspector is its most applicable use among the options presented.