The three films (so far) in the series should be appreciated for their superficial pleasures--action, special effects, moment-to-moment plot. Thinking about the temporal problems too much leads to madness.
Ignoring established continuity, "Terminator: The Sarah Connor Chronicles" works in much the same way; it can be enjoyed for what it is. The Fox TV series seems to ignore the plot developments of "Terminator 3: Rise of the Machines." Jumping from 1999 to 2007, John (Thomas Dekker), Sarah, and Cameron (yet another new Terminator) skip over the action of that film. Also, John’s age doesn’t mesh with “T2.” In 1999, Dekker is only a year (or so) older than Edward Furlong was in 1991. (They jump forward in time in the first episode. Would it have been too hard to just start in 1991?)
"Sarah Connor" delivers thrills in the vein of “T2”--robots chasing cars, robots killing each other, flash-forwards, gunplay, etc. Since cutting-edge special effects from 1991 are cheap enough to be on a weekly series today, the "look" of the show is similar to an expensive feature film.
The new medium supports variations on the established themes of the series. On “monster of the week” episodes, Sarah and John encounter, for example, Terminators on different missions or people accidentally caught up in the main storyline.
And throughout the first season, the serialized adventure allows stories and characters to slowly build momentum. FBI Agent Ellison, curious to a fault, is gradually schooled in the ways of the future. Cromartie is a malevolent Bad Terminator whose head travels through time and—well, it’s sweet, but it takes some explaining.
Watch the show. Just don’t think about it as much as I did.
*Evidently, this is called a predestination paradox.
Forget you ever saw these losers.