One can do that for Mozilla related bugs on bugs ahoy! There is also up-for-grabs using which one can search for issues one can contribute to. See www.firsttimersonly.com for a comprehensive list of resources related to it.
Kent suggested that people who want to encourage people to start contributing
to open source should include the label
first-timers-only on some of the
easy issues which should be attempted only by people for whom it would be their
first pull request.
However, there is no explicit way of keeping a watch out on millions of projects on Github.
Inspired by this movement, I have written a tweet-bot which checks Github for issues with this label and tweets out a link along with the title of the issue. This, hopefully, will help in advertising such issues.
The source code for the bot is on Github: musically-ut/first-timers-only-bot.