The pinwheel is spinning for longer and longer periods of time. Have to manually shut off iMac sometimes to get it to restart.

Question

The pinwheel is spinning  for longer and longer periods of time. Why and what do I need to do about that?

Answer 1

You have 10.6 on that machine, I suggest you stick with it for performance, third party hardware and software reasons as long as possible.
Consider 10.8 (not 10.7) when it's released, because 10.7 and 10.8 will require a new investment in software and newer third party hardware as it requires newer drivers the old machines won't have. (forced upgrade because of software, really nice of them)
http://roaringapps.com/apps:table
Far as your Safari problem do these things until it's resolved:
1: Software Update fully under the Apple menu.
2: Check the status of your plug-ins and update (works for all browsers) also install Firefox and see if your problems continue. You should always have at least two browsers on the machine just in case one fails.
https://www.mozilla.org/en-US/plugincheck/
Flash install instructions/problem resolution here if you need it.
How to install Flash, fix problems
3: Install Safari again from Apple's web site
https://www.apple.com/safari/
4: Run through this list of fixes, stopping with #16 and report back before doing #17
Step by Step to fix your Mac