JavaScript developers often encounter the "Uncaught RangeError: Maximum call stack" error due to recursive functions that do not terminate, leading to memory allocation issues. This happens when recursive functions are repeatedly called without a terminating condition, causing the browser's memory limit to be exceeded. Additionally, handling out-of-range errors is crucial, as certain JavaScript functions have specific input ranges, such as Number.toFixed, Number.toPrecision, and Number.toExponential, which can trigger errors if exceeded. While browsers like Chrome provide error notifications, others like Internet Explorer may crash, emphasizing the importance of validating input ranges during scripting. The text highlights the importance of dry-running code to prevent these errors and encourages developers to be mindful of function ranges to ensure smooth execution.