It seems that there is no definitive reference or rule that specifically addresses whether the adjective "red" in the sentence "Jim wore a red jacket and hat" applies to both the jacket and the hat. However, based on the information provided, it can be inferred that the adjective "red" is meant to modify both the jacket and the hat since they are mentioned together as a compound object. If the hat were a different color, it would likely have been specified (e.g., "Jim wore a red jacket and a black hat").
Therefore, in this particular sentence, it can be assumed that the adjective "red" applies to both the jacket and the hat. However, it is important to note that language and its usage may vary, and there can be different interpretations or preferences in different contexts. Clarity in communication is essential, and sometimes it may be necessary to rephrase or provide additional information to avoid confusion.