I have a 2003 American Series Jazz, 2004 American Series Precision, and 2008 American Standard Jazz V. I also have two American Series Strats, 2001 and 2004. They're all excellent, and most other U.S. Fenders I've tried have been good too. I do think the basses improved with the 2008+ American Standard generation, mostly due to the lighter weight bodies. My 2008 Jazz V is incredibly light and resonant. The others I've tried have been great too, but Bongolation's account of problems in 2011 is disturbing indeed. As far as I'm concerned, that means it's even more important to try before you buy, but it's best to do that anyway.
Or, you could pay a little more and get a G&L JB. The quality is a little better on average, and the finishes are WAY better.