Disable third-party modules that could possibly be interacting with products. Go to the
app/etc/modules/ folder and one-by-one set the active node to false within the xml module configuration file, clear cache after each one is disabled, and attempt to save again.
If this doesn't work, then you need to check to see if any of the core has been modified. Check the
app/code/local/Mage folder to see if any files exist.
Do a diff of the
app/code/core/ directory to an original untouched Magento installation that matches the version you are on.
Check Browser POST/Response data
Also, when clicking to update the product, check your AJAX POST/Response. I use firefox with firebug to do this, but I heard Chrome has an awesome extension that is easy to use. In firebug, I click the console tab and I can expand GET and POST requests along with the Response.