As an aside, I like to look at defensive efficiency for team defense because it is simple - you don't need to worry about "zones" as you do for the Ultimate Zone Ratings and there isn't any kind of subjective, albeit expert, interpretation of what an "average" defender would have been able to do, as in John Dewan's plus/minus system. Quite simply, defensive efficiency is just the proportion of balls hit in play that become outs. If you adjust for the stadium effects, Fenway, for example, would lead to a lower defensive efficiency because balls off the Green Monster are considered "in play", the Red Sox move up to 18th overall, as measured by Baseball Prospectus' Park Adjusted Defensive Efficiency (PADE).
A difference of 3.5% may not seem like a huge one, but over the course of a major league season (for our purposes, about 6200 plate appearances and 5600 at bats, this will vary with the quality of your pitching staff of course) the difference comes out to about more hits dropping in, or over one hit a game. Giving up an extra "undeserved" hit per game is a sneaky way to lose a lot of games. Unsurprisingly, individuals on the Red Sox did not do well if you look at their Ultimate Zone Rating numbers. (Another quick note - I've used UZR/150 in the past, which is a rate statistic for defense over the course of 150 games, in this case I've used the raw UZR values to make it easier to add together in cases where several players played a position). As a team in 2009, the major starters (~30+ games at a position) totaled a UZR of -23.3, or just over -2 wins. Bay (-13), the Lowell/Lowrie third base disaster (-12), and surprisingly Ellsbury in center field(-18.6) were the main offenders.
UZR is harsher on both Bay and Ellsbury than other systems, so their weaknesses may be overstated. The main knock against Ellsbury is that he positions himself too deep in center, in part to make up for his difficulties going back on balls. Several scouts have knocked his route taking as well, which may contribute to his amazing highlight reel of diving plays. While he is an incredible athlete and has the tools to play center field, UZR pegged him as one of the worst defensive center fielders in the game.
In a lot of ways, improving the defense is akin to improving the offense at shortstop. There were three positions where the Red Sox were terrible, so merely improving those to average would see a major gain. Well, the Sox did one better than that, signing the best defensive third basemen on the market (Beltre, 14.1 UZR in 2009) and the best defensive center fielder on the market (Cameron, 10 UZR in 2009). To top it off, to replace Bay in left field they are shifting Ellsbury over. While Ellsbury will likely be an average left fielder offensively, in 80 career games in left field he's been a spectacular defender (10.1 UZR, 21.8 UZR/150). Scutaro is also a slightly above average shortstop (0.9 UZR) another improvement over last year's Lugo/Lowrie/Green three headed monster (-5.7 UZR, although both Green and Lowrie were above average defenders). According to UZR, the Red Sox defense has improved an incredible 85 runs. Even if the offense is worse than last year, which I'm still not convinced will be the case, I just don't see how you could argue the Red Sox are not a better team now than at the end of the 2009 season. Between the starting pitching depth, the elite defense, and the above average, albeit not elite offense, I think you could argue that the Red Sox are best team in baseball.