Have a look in Console found in Applications ~> Utilities, if you can't see a sidebar of logs showing on the left side of the window, click on the Show Log List button.
If you click on “All Messages,” you can look at most everything your machine’s been reporting, sorted by time. The information is organized into three columns; date and time, the sender of the information (which can be a program, for example), and the message itself.
If you open Console ~> Preferences, you can select to be notified when a log you’re looking at is updated, either by bouncing the icon in the Dock or by bringing the application window to the front.
If you like you can create canned searches, just as you can in the Finder (ie: all documents, all pictures etc). To create a canned search, hit Option-Command-N or choose File ~> New System Log Query.
When the query box opens, you can edit it any way you want. If you are searching for a specific program such as Calendar app, reporting an error around a certain time then this is useful. After you hit OK, Console will save your search and place it in the sidebar for easy access.