This started out as a slight annoyance, and quickly got worse.
While it was still - almost - manageable, I went into System Preferences to see if I could turn off or adjust some of the behavior there. That didn't work. I tried attaching a mouse. That worked for about five minutes, before that too was being stymied by the behavior of the trackpad, which was still detecting mouse clicks and presses randomly. It became worse and worse, and operating the computer became an adventure; it was like I had a mad three-year old clicking at things as I was working. Applications I was trying to launch were removed from the dock, other applications were opening unintentionally, and it was switching from one application window to another as I dragged the cursor across the screen. In short it became inoperable.
I did a hurried Google search and found some people reporting a somewhat similar problem after a software update. I haven't updated the software recently, but I restarted the computer to see if that fixed the problem. No such luck.
Then I noticed that the computer was very hot. Very hot. Now MacBooks tend to get pretty toasty when you're playing Flash video, or editing video, but this was extra crispy.
So I stopped using the computer and left it to cool down.
This morning things seem to be back to normal; the trackpad is working like it used to. I'm hopeful that it was just a one-time thing, and that this is not an indication of future problems.
Oddly, I had been recently considering getting something to help cool the MacBook, as I have noticed how hot it's been getting, particularly during these warm summer months. I've been looking at something like this: Cooler Master NotePal X2 Laptop Cooling Pad [$22.99 Amazon]
The reviewers seem to mostly like it; but several have said that the base of the MacBook doesn't really stick to the plastic top of the unit, and the MacBook has a tendency to slide off! One user recommended using velcro to keep your MacBook in place.
If anyone has any experience using these kind of devices with their MacBook (or even other laptops) I'd be interested in hearing.
A couple of interesting posts from Apple Forums:
macbook pro 2011 - severe overheating issues | Apple Discussions
In using your MBP on your lap, you've been ignoring the instructions that came with it:
"Set up your MacBook Pro on a stable work surface that allows for adequate air circulation under and around the computer. Do not operate your MacBook Pro on a pillow or other soft material, as the material can block the airflow vents. Never place anything over the keyboard when operating your MacBook Pro. Never push objects into the ventilation openings."
"The bottom of your MacBook Pro may become very warm during normal use. If your MacBook Pro is on your lap and gets uncomfortably warm, remove it from your lap and place it on a stable work surface."
Trackpad gets stuck on drag mode | Apple Discussions
Sounds to me like your trackpad might be overheating. I have seen this problem before on PC's and MACs. When a trackpad overheats it can at times think that it is constantly pressed down.