There's no Action Center in Vista, but there is this tool: type "problem" into the Start menu's Search box to use it. Click "View Problem History" to see a list of all current and past problems. Click OK and click "Check for new solutions" under Tasks.

Vista will upload all of the problems listed – if prompted, send more information, which may help provide a solution. If you're lucky, you'll be told solutions have been found; click one to review its findings – you may be told to download an update, take a specific course of action, or go to another site for more help.