How amazing... I have EXACTLY the same problem...
My Rig
Macbook Pro 15", Mid 2009, 2.66 Ghz. (Dual Graphics - GeForce 9400M & GeForce 9600M GT) running OS X 10.7 Build 11A511 - The Gold Master and eventually Retail version.
I have been running Snow Leopard and its subsequent updates, since its release. I have never had any issues with it at all, it was just the idiosyncrasies of the 3rd party software that would cause problems, but only minor, By the time Lion came around (I am a Developer so I got the GM in early July) I actually had a very stable rock solid computer
I am very methodical backing up, so when Lion was publicly released, I did the final Snow Leopard Migration assistant update, did a complete time machine backup.
I noticed that the build of the newly released Lion was the same as the development GM, so I decided to do what a normal customer would do, download it from the app store and install it on my now very stable Snow Leopard installation.
After the download finished, I clicked the install, nothing else and as per normal, thirty or so minutes pass and a restart happens, Lion is installed successfully over the top of my Snow Leopard.
Now here is when the problems started :-
When Lion booted, I just got a gray thatched screen, the login window was obviously there bust I couldn't see it, so typing blindly, I typed my password and the computer then loaded up my user account.
When that had finished, It looked nearly identical to the old Snow Leopard (a good thing). but when I clicked and dragged ANYTHING, in the Finder or in an App, what ever I was dragging stuck to the cursor and will not go away. I had to force quit the Finder or the App in question to get the cursor to "drop" the icon. (The problem in this thread)
the Second issue, was nothing with video or photos displayed... If I launched Safari 5.1 for example, and go to YouTube, the YouTube page would load, but as soon as it finished, It would flick to a blank white unclickable page.
Even the System Preferences were effected... If I went to Desktop & Screensaver the screensaver examples would just be a white box, nothing in them.. Desktop pictures were white. Even in the Finder, all the ICONS were white boxes.. no matter which view you put them in...
So these 2 combined issues are are pain...
anyway I solved the white page / Icons / screensaver / Flash / Youtube / problem by going to System Preferences, Energy Saver and turning the Graphics option to "Higher Performance"
If you have it set to "Better Battery Life" - the white screen problem reoccurs.
So I am now at the same stage as all of you. I have icons, text, browser elements, etc all sticking to the cursor when I go to drag them.. They just will not let go..
My temporary workaround :-
Create another user account on your computer
Log into yours (which will be experiencing the stuck icon issue) then just switch to the newly created account and back to yours again.
That fixes it...I don't know why, but it does.
I tested it the other way as well... If you log into the newly created account first, it WILL experience the sticking icon problem.. Switching to your account and back again, fixes it...
All of this is really unnecessary and totally annoying... so I hope someone figures out what the **** is going on... I don't want to keep switching accounts every time I boot up the laptop...