The ./manage.py validate command has been replaced with ./manage.py check in Django 1.7. The new system checks framework [1] is extensible, so third party apps will be able to add their own checks.
Searching the tickets that require documentation [1] or unit tests [2] can be a good place to start. It's a sign that a bug or new feature has been accepted, and that the patch can be accepted with some improvement. If a ticket is assigned to somebody, but hasn't been worked on for a few weeks, then don't be afraid to pick it up and improve it.
If there are any sprints happening near you, then go along. Daniele Procida runs a workshop Don't Be Afraid to Commit, which covers a lot of the basics you need to write your first Django patch (git/sphinx/...). The workshop is online [3].
There's a low traffic Django Core Mentorship mailing list [4] that you could join, or #django-dev on IRC might be helpful.
Good luck!
[1] https://code.djangoproject.com/query?status=!closed&needs_do...
[2] https://code.djangoproject.com/query?status=!closed&needs_te...
[3] https://dont-be-afraid-to-commit.readthedocs.org/en/latest/
[4] https://groups.google.com/forum/?fromgroups#!topic/django-co...