THE ESSENCE OF THIS USC BUG is that USC fails silently and inexplicably leaving the new user (the target audience for Ubuntu Software Center) in the dark as to what to do next.  Below are listed least three slightly different circumstances that result in this bug.
.  
FIXES: 1) Minimally the USC needs to give a) meangful error message that b) provide a course of resolution action doable by a new Ubuntu user.  There are probably always going to be circumstances where USC will fail so *at least* meaningful error messages are always going to be a bottom line requirement.
2) Even better would be if USC attempted to resolve the underlying issues that are triggering the bug.  So if it is an apt-get problme maybe running running apt-get -f install . (For more see http://www.linux.com/archive/feed/48910 for an escalating solutions for when apt-get fails).
3) One easy partial 'fix' that at least sometimes will avoid triggering the bug is to change the default to have the application menu item run with 'gksudo softwarecenter' instead of its current default which is simply 'softwarecenter'.  This would avoid some of the policykit errors.  


3 TRIGGERS/WORK AROUNDS FOUND (SO FAR):
1a) In the quarkrad's forum post ( http://ubuntuforums.org/showthread.php?t=1500473 ) according to post #18 he said it  "appears a policykit startup program was launching a KDE rather than a gnome version."  He did a workaround by
[quote] 
 "System/Preferences/Startup Applications
 
 Under the Startup Programs tab uncheck PolicyKit Authentication Agent. Click on Add to create a new startup program. In the    
           Add Startup Program window enter the following in the Command: box - 
 
 /usr/lib/policykit-1-gnome/polkit-gnome-authentication-agent-1
 
 In the Name: box give the new startup program a name -I called mine gnome Policy Kit. Click on save and have this as the new 'policykit startup program'. I can now install programs from the Software Centre.
[/quote]
 
1b) Hazbeen in the same forum thread, reports this workaround worked: 
  "Go to: System> Prefs> Main Menu> highlight the Software center, click properties> add "gksudo" without quotes to the beginning of the Command"

1c) GMos'  bug report post #7 above described a similar policy kit error resolved by running 'sudo'.

2) In the same forum thread  in post #15  urobb reports being able to resolve the issue by removing "ubuntu-restricted-extras" from the repository list.

3) Ken Anderson reported extremely similar symptoms but in addition had to resolve some kind of issue apt-get was running into (possibly with previously incompletely installed packages) resolved by 'sudo apt-get -f' first.  Then Software Center resumed normal functioning.

Ken Anderson reports (post #8 above) he's using: 
 OS: 10.04 lucid,  
 apt 0.7.25.3ubuntu9, 
 Ubuntu Software Center 2.0.5

And Ken reported 7/4/2010 on the #ubuntu-beginners irc channel as philw zkriesse duanedesign and newboon2age were assisting him (excerpted from http://irclogs.ubuntu.com/2010/07/04/%23ubuntu-beginners.txt )

[19:55] <win_2_linux> software center, synoptic nor apt-get is working

software center and synaptic start then go gray and quit

Tried apt-get upgrade because the upgrade manager doesn't work either:
 bus errordependency tree

USC from terminal:
  /usr/share/software-center/softwarecenter/apt/aptcache.py:40: GtkWarning: gtk_container_add: assertion `GTK_IS_CONTAINER (container)' failed
 gtk.main_iteration()
 Bus error

Ken then tried solution  
Result:
 still grays out and quits

gksudo software-center:
 starts up, turns gray and quits
 doesn't ask for password, apt-get doesn't work either nor synaptic nor upgrade center 

sudo synaptic: 
  bus error

(sudo?) apt-get: 
  dependency tree errors bus error

$ sudo apt-get check
Reading package lists... Done
 Bus errordependency tree... 0%

sudo apt-get -f install
 ok things worked