The three sentences that follow illustrate the importance of the inclusion or omission of a comma can have in easing comprehension of a sentence.
1. After two hours at the bar, Jones said Smith was too drunk to drive, and Smith insisted that Jones take him home.
This sentence erroneously implies that two hours after Jones and Smith arrived at a bar, Jones made the statement (to Smith?) that Smith was too drunk to drive; it seems odd that after Jones confronted Smith, the latter would demand a ride home. However, Jones is relating, much later (and to another party), the fact that two hours after they arrived at the bar, Smith was too drunk to drive; his demand for a ride was not in response to a confrontational comment.
Inserting a comma after said to make “Jones said” a parenthetical attribution clarifies that Jones made the statement later, not that night: “After two hours at the bar, Jones said, Smith was too drunk to drive, and Smith insisted that Jones take him home.”
2. Smith admitted that he knew about the design side, but he didn’t know a whole heck of a lot about the manufacturing side.
As written, this sentence suggests that although Smith acknowledged aloud that he was familiar with design, he apparently kept to himself his ignorance of manufacturing. However, though the context is not clear in isolation, Smith gave both pieces of information. In order to communicate that fact, the two components of the sentence must be parallel (“he admitted this and that”), and the comma must be omitted: “He admitted that he knew about the design side but he didn’t know a whole heck of a lot about the manufacturing side.” (A repeat of that can be inserted after but, though it is optional.)
3. This is the final known image of actor Robin Williams posing with a fan.
This caption accompanying a photograph of Williams and an unidentified person can be read two ways: It is the last one he took with an admirer before his death (and the appearance of another person in the photo is important), or it is the last photograph taken of him before he died (and it just happens that it was taken with a fan).
Even out of context, the first interpretation is suspect; unless the article the photo accompanies specifically pertains to the distinction of Williams being photographed with a fan (not likely), it’s almost certain that the fan’s presence in the photo is irrelevant to the distinction of the picture as the last one known to feature Williams before his death, and the phrase “posing with a fan” should be treated as a dependent clause: “This is the final known image of actor Robin Williams, posing with a fan.”