I recently downloaded updates for Adobe Photoshop Elements 9 for Mac. Now, when I select "SAVE AS" then select a format, such as JPEG or Photoshop file, the appropriate extension is NOT ADDED to my file name.
There is a known bug that is causing the issue you are encountering. It has to do with the Preferences. Basically, what happens is this: if you go to Photoshop Elements>Preferences>Saving Files and then click OK (regardless of any options changed whether in Saving Files or any other preferences sections), the option "Append File Extension" will change to "Never".
Currently, there is only one way to fix this: Recreate the Photoshop Elements Preferences. This can be done by holding Command+Option+Shift while launching Photoshop Elements. If you time this right you will see this dialog:
(if you don't see it, try again).
There is only one way of avoiding this bug: do not visit Photoshop Elements>Preferences>Saving Files and click OK. Visiting the rest of the preference topics is fine. But if you go to Saving Files you must cancel out of the Preferences to avoid this bug.