Broad didn't really make his name in the West Indies because not many people watched much of the cricket. Quite understandably too. Hence there was a period where everyone was insisting he was useless and very few of us were defending him.
I wouldn't say he was magnificent, but he justified his place for the first time. The pitches were unbelievably slow, the West Indies (and their groundsmen) were content to play for a draw after taking the first test, the weather was quite a bit too hot for cricket and for some reason Ramnaresh Sarwan temporarily turned into Don Bradman for the entirety of the series. For the Antigua test England had no supporters at the ground because it was shifted a few days forward after a pitch-related balls-up, but after going 1-0 down in a series they were very much expected to win, the fans and media were more likely to get on their backs and question their places in the side than offer any encouragement.
Broad certainly didn't tear the place up, but he did manage to keep the quality and pace of his bowling notably high for spell after spell when any reasonable person would have gone bat**** crazy out of frustration. This compared particularly well with Harmison and Sidebottom, who totally embarrassed themselves, and it was incredible how many people were still advocating bringing them back in place of Broad over the course of the following summer.
I think he should probably be dropped for the first test because he's not bowling well and England have plenty of alternatives at the moment. But I do think it's worth remembering how well he performed in what was a seriously, seriously nasty tour to be a bowler on. I tend to focus heavily on more recent events when it comes to assessing players, but since it came up, anyone who questions how flat the pitches were or tries use the fact that England never took twenty wickets in the series as an argument against Broad's capabilities as a bowler really obviously just wasn't watching.