Puyol killing it in the rehab center, yeah. He spent more time there than on the pitch during his last few seasons, and instead we saw the horrible Mascherano in CD instead, and some times Busquets.
During 2010-11, Puyol just made it back after a long time injury for one of the Madrid clashes in the CL semi finals, only to instantly get injured again during the very same match, and gone again for months. And Abidal was, as you may recall, out for a long time during this season due to cancer treatment.

Before Pique joined, Puyol was much less injury prone, but was teamed up with the likes of Sylvinho and Milito... Ugh Milito, still gives me nightmares.
Alves was definitely the best RB, but more for his offensive capabilities. The way he played often created problems for the defense if they lost the ball. And you really don't want to get caught in the counter attack with Milito or Mascherano in center defense.

Guardiola said it as well that their defense was never good, but they made up for it with their offense and possession play.
Barcelona's defense has been notoriously lacking for quite a while, especially compared to other top clubs. They didn't even sign a single center defender ever since Pique until this season. They bought Mascerano and Song, who are naturally defensive midfielders, and tried to re-school them into becoming CD's instead, which didn't work.

Brazil of today is much more defensively focused than Brazil of old. How many good well known attacking Brazillian players are there these days compared to good well known defensive? There's not as many, while the very best Brazil teams have almost no memorable defenders or goalkeepers the recent teams have seemed to be centred around those types of players. While I agree their coaches suck I think that is because they are all overly defensive and not capable of playing the kind of good attacking football that Brazil are known for and that wins trophies.

Ah yeah, I meant Marquez. Mixed them up. And Milito didn't play much, yeah. But the problem was that when someone gets injured, Barca only had players of Milito's caliber on the bench, or they move other players down from their natural position into defense. Barca's defensive problems over the years basically came down to two things. Puyol's increasing injuries, and Pique's stagnating form. (He's been good this season, though.)
When Barca won CL last time for example, Puyol didn't even play half the CL games, and the ones he did were primarily in the group stages. With the substitutes Barca have, that's quite scary when moving on to the knockout stages. And that's what I've come to get used to over the years. Of course he wasn't there when Barca got slaughtered by Bayern two years ago either. Instead they had to use the very young and untested Marc Bartra.
And I was never fond of Mascherano in defense. He's usually late in challenges, awarding clumsy cards and penalties. He's a fantastic central midfielder though, as we saw in the World Cup. But I'm always worried when he plays in defense. Same with Song, Busquets, or whoever else gets forced to play there.

As for why they bought Mascherano and Song, since Mascherano and Busquets basically played the same amount of games each season since he came to Barca, and they played nearly all of their total matches, Mascherano spent the vast majority of that time in central defense, since Barca don't play two defensive midfielders at once.
Perhaps the primary intention was for him to be Busquets substitute, but it was barely ever neccesary, and instead he was constantly needed in central defense. So you'd have to ask yourself why Barca didn't buy a central defender for so many years when it was obviously much more needed than midfielders or forwards, who they had an abundance of, both from signings and from the youth system.
As for Song, I think in his case a big reason for why they bought him was to turn him into a CD, because with a midfield lineup of Xavi, Iniesta, Busquets, Cesc, Thiago and also potentially Mascherano, his chances of getting to play there weren't very high.
I always found that signing very strange.

Premier League teams with their shitty defense wouldn't be a bump for Messi.

That's why I said 'some'. Tell me, how has Falcoa done this season? What happened to Shevchenko? It is known that many footballers that do well in Europe struggle in the Prem, well sometime not struggle but get nowhere near the same performances. This said, I mainly want to see him in the Prem to see him in the Prem week in week out, I don't watch Spanish football. :P

I think he joined at 29, his first season he played most games but didn't score many. Van Persie is currently older than that, has had serveral injuries while at Man U this season and still has more goals this season than Shevchenko did in 3 years in the Prem.