Could a persistent cough in a smoker be something to worry about?

Yes... Persistent cough in a smoker could be a sign of copd. If the cough is productive, chronic bronchitis may be present and if non-productive, empysema may be present. Either way, you should see your doctor for evaluation and treatment. Smoking cessation is absolutely necessary and your doctor can also help with this.
Persistent Cough? Smoke; no smoke -persistent cough requires a closer look-see. Although a good reason to stop smoking, very wise to make sure there is no post nasal drip, small polyp or allergen that might be causing the problem. Even nervous tics, stress signs can cause irritation.
Cough in smoker. A persistent cough in a smoker is something that needs to be investigated. In those who smoke, we have another layer of concern in regards to a chronic cough. Emphysema? Chronic bronchitis? Cancer? This cough should not be ignored. And stop smoking!