Note for Mac OS X Mountain Lion and Mavericks users
Apple has imposed new restrictions on installing unapproved applications on Macs starting with the two most recent versions of Mac OS X, 10.8 (Mountain Lion) and 10.9 (Mavericks). As standard, only apps by registered developers can be installed; you will need to turn this feature off to run QTM. Registering costs money, which I cannot afford at this time.
Go to "System Preferences" (in the Apple menu) and click "Security and Privacy" in the top row of icons. Click the padlock icon at the bottom of the window, then enter your password. In the menu that is headed "Allow applications downloaded from", click the entry that says "Anywhere". It will give you a warning and tell you an alternative way to run an unapproved app. However, this removes the restriction until you change it back.
Alternatively, you can right-click on any application icon to run an unapproved app like QTM. I am not sure if you can still drag it to the Applications folder if you do not disable the new security feature; you might have to drag it to your home folder.
When compiling from source using Qt 4, you will get warnings that the version of Mac OS X you are using is unsupported. You should ignore these warnings (however, Qt 5 is recommended on the Mac).