A google search shows that this bug (or, "these bugs") are being widely discussed. Understandably. We generally do not expect such shotty releases that result in this significant of a degredation in performance -- and most importantly, usability -- with Apple products. It's at once a testament to their general development history, and an admonishment of their current screw up.
I used Process Killer to monitor memory usage on my iPad, particularly when apps crashed during start up. I found that every time the apps crashed, memory usage at was nearly 100% -- with "Wired" memory (memory required for the OS and graphics) consuming as much ~180mb. Even with minimal apps running in the background I rarely had more than a few mb of free memory available.
What appears to be happening is that when apps are launched, there's simply not enough free memory available to even initialize the data/graphics/etc at startup.
I've have since turned off iCloud services (deleted the account entirely) and things are back to running relatively smooth. The wired memory consumption immediately dropped to ~100mb, freeing up the difference. I'll update this thread if things change.