I downloaded a great presentation and transcript from a January 2008 briefing for JPL Solar System Ambassadors on the James Webb Space Telescope (JWST). Unfortunately I couldn't attend the live telephone briefing, but I learned a lot from the presentation and the speaker's transcript. It's quite an amazing project, and when it is launched in 2013, it will certainly be a worthy successor to the Hubble Space Telescope. I found an earlier version (May 2007) of this talk by STScI's Knox Long here (~2.6 MB PDF).
JWST will operate in the infrared and will have a much larger primary mirror than HST, as shown in the graphic above. It will also be vastly more complex. I was talking recently with a colleague who is involved with the validation of the optical fabrication, assembly, and testing plans for JWST. As you might expect, NASA is not taking any chances on a Hubble-type mistake, and there are checks upon checks upon checks, with close attention paid to the assembly and test procedures and the testing optics (which were the source of HST's troubles). But the tolerances are incredibly tight (he mentioned that one engineer cheered when he learned of a particular tolerance that was about the thickness of a sheet of paper - such an unusually huge tolerance would be easy to achieve, but most tolerances are much, much tighter). The number of interacting systems and the number of items in the error budget are simply immense.
In addition to the usual problems of precision optical fabrication and the vibrations and stresses of launch, JWST must maintain its precision through a complex automated "unfolding" in space, and must operate at cryogenic temperatures. To stay cool, it will operate at L2, a special orbital point far beyond the moon. So a Hubble-like service mission will be essentially impossible. It will be possible to do various adjustments on-orbit, but it basically has to work "right out of the box" (or launch shroud).
When they say this project is challenging, they are not kidding. Will it be ready to launch by 2013? Everybody on the project is working to anticipate all the possible problems so it will make the date and work perfectly - but there is still a long road ahead.