Trac is the place to follow along with the development of WordPress. You can view recent code changes in the Timeline section of this site.
If you are looking to submit a bug report, please head on over.
You will automatically receive notifications for tickets you have reported or participated in. If you would like to receive notifications for any other ticket, click the star next to its summary to "watch" it.
You can browse the source of WordPress here, but you probably also want to install a development version of WordPress locally.
If you have encountered a security issue that isn't addressed in a released version of WordPress, please contact the security at wordpress.org email address with detailed information. For more, see our Security FAQ in the handbook.
There are many ways to contribute to WordPress. We have a detailed contributor handbook to help get you started.
If you want to get started quickly, test a patch, or grab a bug and see if you can reproduce the problem it describes. Don't miss the PHP and JS unit tests — and if you like writing unit tests, there are some tickets that could use them.
Follow the Firehose
There is also an RSS feed and an automatic mailing list to follow allow with every single discussion on Trac, but be aware that these can be very high traffic (dozens of messages per day). You should probably just subscribe to the individual tickets that you're interested in.