Answer: The problem that is illustrated by the sentence provided is "grammatically incorrect".
Step-by-step explanation: The sentence "I joined the others by the fire however they were about to go to bed" is grammatically incorrect because it contains punctuation mistakes. The sentence provided includes a connector ("however") that is joining two independent clauses. Punctuation rules state that a semicolon must always be added before "however" and that a comma must always come after it. In that way, as the sentence provided does not include a semicolon nor a comma, the sentence is grammatically incorrect. The correct way of writing it is: "I joined the others by the fire; however, they were about to go to bed".