Here's my input. iPad2 IOS 7.0.6 - 11+GB free space. All apps have been updated. I reboot frequently, but it doesn't solve the problems.
Absolutely everything regarding app switching worked perfectly BEFORE upgrading to IOS7. Every single app I used worked flawlessly. Multitasking and several apps do not work correctly since, and I am now on 7.0.6. I've tried all the recommended settings to get rid of parallax, app background updating, etc. Nothing works.
Examples:
Word Numbers: They freeze up EVERY TIME I open or return to them. There is a five second or so lag - frozen.
(Tried turning iCloud off, but that didn't solve it.)
Safari: Will just close itself several times a day. I also experience the multitasking issues mentioned in this thread.
I love my iPad2. I absolutely hate IOS 7. It ruined a wonderful tablet. Besides the issues in this thread, the update brought my spiffy iPad2 to a crawl.
I'll wait for 7.1, but if this persists, I'll be buying an Android tablet. It might not be any better, it might be worse, but at least it isn't so boring looking.