Open Console, found in Utilities. This program is used for viewing all the different logs the Mac maintains for diagnostic purposes. On the left column, under System Log Queries, make sure All Messages is selected. Take note of the time at the last line on the bottom of the messages on the right.
Leaving Console running, insert your DVD and try to play it.
Now go back to Console and select all the messages that appeared as result of your action. Use the timestamp to position yourself in the list. Copy all those messages and post them back here for diagnosis.