Rec was filmed from the point of view of the cameraman - although I'm not a big fan of Michael Bay-style shaky-cam, it worked well in the movie; it provided a sense of immediacy that amplified the tension.
Rec 2 (2009) picks up a few minutes after the first film. An armed quasi-military squad (think SWAT) are asked to bodyguard a researcher and another cameraman while he collects a sample of blood from the building. Of course, things go very bad very quickly.
A rather unexpected diversion in the film introduces three teenagers; they're goofing around with a video camera, when they make a bad decision and find themselves trapped in the apartment. The kids are annoying in a way that only kids shoe-horned into a movie can be (i.e. destined for peril), and serve as a minor plot point..
The end of Rec implied a religious connection to the contagion, and this is further amplified in Rec 2. The researcher turns out to a be a priest involved in fighting this outbreak of demonic possession. This gives Rec 2 a certain 1970's old-school feel (which isn't necessarily a bad thing). This may have resonated more in largely catholic Spain, but I had trouble accepting this at several points (especially during the Exorcist-like interrogation of one of the teenagers).
The shaky-cam is shakier, more so in the action scenes and sometimes it's difficult to adequately tell what's happening to who. It's not overly annoying, though; if the filmmakers wanted viewers confused and disoriented, it worked. There's certainly some inventiveness - a zombie is dispatched with a firework thrust down its throat, leading to a remarkable scene in a dimly-lit corridor; the shaky-cam highlights the shear anarchy of what we're witnessing.
The slow build-up of the first film is largely discarded, and there's more Zombie-huntin' with guns. It doesn't have the sparse, linear, plotting of the first film, but chooses to throw in a few curve balls.
The ending implies that the demonic contagion will spread to the outside world, and sets up the premise for Rec 3. If Rec 3 retains the immediacy and intimacy of its two prequels, I can see it being a success with genre-fans.