
Can we assume that there's some truth to what the film dork in Scream 2 said, that trilogies are good but sequels suck? If so, no matter what people say, Infernal Affairs III gets the short end of the stick.
The plot in itself is decent. The bad guy from the first film is slowly being hedged in by under-cover agents at the police station, and its coordinated with some sort of fun Hong Kong - Mainland intrigue. Like the second film, but not the first one, the plot is a bit convoluted, which works for this film, because unlike the second film, it uses the same actors as the original.
My problem with this film is that the film does not fit in to the overall message of the first film, and therefore comes across as something of a shameless ploy to make money off a brilliant film. The first film was an ironic tragedy, that was perfectly structured as a Buddhist parable. The second one was entertaining but nonsensical eye candy that did little damage to the first film because it had fairly little relationship to the first film. This film unfortunately added to the first film by taking a tragic ending with a beautiful message (that there is such a thing as a 'horror of living'), and changing to the cliched message that bad people eventually get their due, which is a horrendous debauchery of poetry (I feel silly saying that, but its true).
I do though honestly think that this film is worth watching, just not as a sequel, and the connection to the first film should be minimized in ones head. The convolutions of the plot are quite entertaining to watch, and it is an entertaining film in that Hong Kong type way. Not to mention that Andy Lau and Tony Leung are monstrously good actors.
Infernal Affairs was a great movie that will hopefully still be watched decades or centuries now, Infernal Affairs III is a decent Hong Kong flick to be watched for entertainment.

So a funny thing happened when I watched Infernal Affairs II... I had no god damn clue what was going on. I want to put my notes on the film up following my notes from the first one, but given this little deficiency I'm not sure if I can provide the deep analysis (musings?) that I like to provide.
The movie was a prequel, using different actors, so I had no clue who was who, and I in fact didn't really even get that it was a prequel until later when I realized that the actors were the same as the flashbacks from the first one. The plot is labyrinthine, the cops and the thugs from the first movie team up to kill some thugs from another movie, the gangster who joined the police force from the first film, falls in love with/kills the crime boss' wife (all men kill the things they love), other than the vaguely similar characters its connection to the first movie is rather sparse. There is a lot of conspiring between the police chief and the crime boss, to do some sort of manipulation of the underworld. Its all set to the end of the British occupation in Hong Kong, and that whole "end of an era" feel.
I did enjoy this film though, the acting, as is usual for this series, was all superb, and I have a certain affection for labyrinthine plots (Raymond Chandleresque, not films that don't make any sense, like the matrix). I also like that it reworked the "cops vs. thugs" story to a cops with thugs story. A much different version of the "if all these radios go of" monologue from the Asphalt Jungle.
The real problem with the story is that nothing in it is really developed fully enough. Even the driving force of the film, the relationship between the police chief and the gang boss is only moderately developed, the plot is too complex to interesting as anything but a backdrop (as in a Raymond Chandler story), and the characters you are attached too from the first film are mostly absent. The film is filled with charming moments. Anything with the gang boss is lovely, and the undercover cop does does nice things, but its not enough to the film focused. The only thing that really grabs the attention and holds it, is the affair between the undercover thug and the crime boss' wife... which is beautiful
Basically I'm saying, its worth watching, quite worth watching actually, enjoyable to watch even, but not for the story. Just for the way people move.