For a few months there's been a Mesa "Newbie Projects" listing done by Mesa developers (in particular, Ian Romanick at Intel has been spearheading this initiative) with lowering the barrier to begin contributing to Mesa. The projects are often generally easy and the details shared on the Wiki nearly walk new developers through the process step-by-step.
This Mesa Newbie Projects initiative has yielded contributions from new developers in the few months that it's been around. The project list was recently updated and now there's another set of patches from a new developer looking to cross an item off the list while getting his feet wet with Mesa development.
Rafal Mielniczuk published five Mesa patches (plus separate Piglit regression test cases) for the GL_NV_non_square_matrices extension to OpenGL. This extension adds non-square matrix support to OpenGL ES 1.0/2.0. Non-square matrix support was added to OpenGL ES 3.0 and has been in the desktop OpenGL standard since the OpenGL 2.1 days. This project was basically to open up the non-square matrix support from desktop OpenGL already present in Mesa to making it available as an extension in the earlier OpenGL ES versions.
Rafal Mielniczuk's patches are currently found on the Mesa-dev list and have yet to be reviewed (or merged) by any Mesa developers. There's also some similar OpenGL extensions that can be implemented in a similar manner to the GL_NV_non_square_matrices extension for new developers wishing to get involved. Other easy projects for Mesa can be found via the Newbie Projects list.