He came into Test cricket far too early, and is now starting to warm to the task. Michael Holding had the same problem. Was brought in far too early, and his record early in his career was poor, but as he gained experience he improved immensely. Not saying that Broad will be as good as Holding, but it's not completely impossible.
New Zealand and West Indies are not minnows either. They've got some very decent batsmen, West Indies had the best batsman in the world when we played them in the Windies. Chris Gayle is a very good player, as is Ramnaresh Sarwan, and Brendan Nash was impressive as well. They're nowhere near as bad as you make them out to be, so simply dismissing performances against them is incredibly harsh.
The reason Broad hasn't got wickets in this Test is because he's bowled poorly, not because Australia are miles better than anyone else he's played. He can bowl far better than he has, and you're just plain ignorant if you can't see that.