OK, after re-installing 10.8 and some more systematic testing, it looks like the issue with dock animations and click and drag are NOT related to my Canon scanner or the software that came with it. It seems to be an intermittent but oft-repeating bug with 10.8, and I'm not the only person who's got it. On the up side, putting my iMac to sleep and immediately waking makes the problem disappear for a while, but I've had to do that four times today.
Last August is the Stone Age? In any event, I just checked the Canon site--the driver I'm using is the most current one available. As I indicated above, my trouble no longer seems connected to my scanner or scanner software.
My MP Navigator EX is 4.0, and I can't remember since when, it's a looooong time ago I updated it, and 1.5 moons ago I went to 4.0.3 to make it work with Mountain Lion. Just saying...
Once you're at it, consult your Login Items list and be surprised what you find there. But if you insist, it's all irrelevant, of course. Just saying...
Leaves the following suggestion (because maybe there's some old stuff left in the system from the days before updating to 10.8.x):
1. Back up.
2. In System Preferences -> Print & Scan, reset the printing system (right-click on a printer, find it in the context menu).
3. Find and delete any Canon scanner apps under Applications.
4. Go and manually find and trash anything related to scanner in the Root/System/User Libraries, (prefs, drivers, anything).
5. Delete anything related from the Login items list in user accounts.
6. Restart Mac.
7. Re-install scanner (via Print & Scan) and software from scratch.
Probably needless to state, but I wouldn't be surprised if after point #6 the funny drag & drop effects had ceased. If not, you may also reset the SMC, and if it doesn't help, trash the Finder and Dock prefs if you haven't yet.