First of all, BB and crew have been drafting for fourteen years, so this discussion splits into pre BB and BB. Probably Ken Sims, Eugene Chung, or Hart Lee Dykes are the worst first rounders pre-BB; these are high draft picks who couldn't or wouldn't play. But they are from twenty-plus years ago.
Most of the first rounders of the BB era have produced in some manner. Obviously the worst drafting error is picking a guy with no talent in the first round, and they haven't really done that at all. The team is going to play the first rounders, so guys like Maroney and Meriweather, who didn't make it to their second contract here, belong in this discussion because they seemed not so good but still played a lot. Meanwhile, guys like Andy Katzenmoyer, who maybe could play a little but got injured in his first season and left football, or, less on point here, Robert Edwards, who looked like he could play but got hurt and was done, are ranked below the talent-light crew, but BB hasn't really had any of those in the first round either. The second round failures, like Chad Jackson, Ron Brace, Adrian Klemm and Terrence Wheatley, are less egregious because that's a place where teams take a flier on an injured or otherwise questionable player. But clearly that's from where many of the failures have come.
Overall, Chad Jackson was the least effective draft pick. A high second rounder (#36) who couldn't play. What a dog. He was pretty hyped during the 06 draft too, and it was surprising that he slipped to NE. 18 NFL games, that says it all.
A strong case could be made that Laurence Maroney is the worst BB first round pick. He is the only BB first round draft pick thus far to have completed his career having played less than 100 games (he played 49
http://www.pro-football-reference.com/teams/nwe/draft.htm. ) He was an RB, which position has the shortest average career due to the wear and tear of the position but still, the next shortest career is Brandon Meriweather's, at 89 games, and he is still active. As we all know, Maroney could play, but he didn't want to play the way BB wanted him to, then he got hurt at the end and couldn't really catch on anywhere else.
Ras-I Dowling fits in with the injured crew, he was not a successful pick by any means (8 games thus far) but the failure level on the that pick gets discounted because of other successes NE has had drafting injured college players, like Gronk or Curtis Martin (third rounder).