Facebook and Twitter integration not working

Question

I'm have trouble using Facebook and Twitter integration in Mountain Lion. When I click 'Click to Tweet', or 'Click to Post', nothing happens; I don't get the notecard looking thig, and it's like I never clicked the button. Same thing with sharing from an app, except for Twitter. I receive notifications from both just fine, but I'm unable to post. I can tweet something from the sharing menu (link to a webpage with Safari, for example), but I cannot send a tweet using the 'Click to Tweet' button in Notification Center. Also, I cannot post to Facebook by neither sharing nor the 'Click to Post' button. So far I have tried sharing with Safari, Finder, and Preview, all with the same results. (Facebook sharing with iPhoto does work, but I don't believe that is integrated with OS X.)
I have also tried the following, with no luck:
Checked my settings on the Facebook and Twitter sites.
Removed my acounts and re-added them.
Obviously, my internet connection is working.
Added my Facebook account to the 'Guest User' account, and another administrator account.
Had a friend add his Facebook account to his own (limited) account on my computer--he could not post to Facebook either.
I believe the last two things I tried indicate that this is a system-wide problem. A couple more things to note: 1) there is no kind of error message; it just sits there, like nothing happend, no 'spinning wheel' or anything. 2) It DID work before. Twitter worked when I first upgraded to Mountain Lion, and Facebook worked when I installed the 10.8.2 update. I don't use either often enough to know when exactly they stopped.
Here is a video illistrating my problem.
It's been driving myself crazy with this over the past few days, and can't seem to find an answer anywhere. I also seem to be the only one with this problem.

Answer 1

First, I would eject whatever it is that you downloaded. Go to Finder and eject it that way or depending how you have your system set up, do the two finger tap and Eject it. Download the link above. Once it downloads, double click it to install it. It should work. If it doesn't you need to use your Disk Utility to check for errors. Click your Finder again and then Applications. Scroll down to Utilities and then Disk Utility. Click on your hard drive and you will get a menu of items on the right side. Towards the bottom, you will see a button to Verify Disk Permissions. Click that and let it run. It may take a few minutes to finish. Once it's finished there may be a list of things wrong with your system. Click the Repair Permissions and let the computer do it's thing. Use Disk Utility at least once a month to make sure everything is in order on your system. If this doesn't fix it, I don't have any other suggestions. I'd hate to say do a fresh install but that might be the next step if this doesn't work.
Something else to consider is that is if you use Time Machine and the system did work at one point, you could go back to the last known good point and reinstall that back-up. You would lose anything you have saved since that point (obviously). If you take steps to back up your information, that should not be an issue. (For me), Time Machine works as advertised. If you are not backing system up regularly, shame on you. You need to start ASAP backing up. It's an easy process and it's times like you are having now, that make the small preventive maintenance, worth extra time and effort.
Good luck.