If you migrate from a previous machine to a new machine using Apple's Migration Assistant, and in the process you create a new user -- this can happen if you create your old user account on the new machine prior to migrating -- you may have issues with Firefox and the Downloads folder. Because of a shortcoming in the migration tool, the OS X Downloads folder for the new account will have the path for the old account, and Firefox will then be unable to save because it does not have the correct permissions. I encountered this issue with 10.5 Leopard (both machines), migrating from an old Mac mini to new Mac pro.

The solution is to open ~/Library » Preferences » com.apple.internetconfig.plist with the Property List Editor (Xcode required), navigate to the Download Folder item, and delete the value (not the key; just the value under it), then save the property list file.

The next time you save a downloaded file in Firefox, OS X will ask you where you want it. Answer the question, and the problem goes away permanently.

[robg adds: A commenter on the queue review site notes: "This is a bug with Firefox that I see with our users all the time. In prefs, the download folder looks like it's set correctly, but Firefox wants to download to some read-only folder on the hard drive (it's always arbitrary). We have had to delete ~/Library » Preferences » com.apple.internetconfig.plist -- but we ALSO have had to delete ~/Library » Preferences » com.apple.LaunchServices.plist to resolve it."]