Flare control is average in the Sigma 19/2.8 EX DN lens. You can observe that the lens shows some flare and color streaks across the frame in situations when a strong light source (in this case sun) is within the picture frame. Overall however, this is not a terrible result, given the focal length of the lens.
Sigma showed moderate levels of vignetting on NEX-7. At f/2.8 light falloff reaches ~1.5px (uncorrected) but drops to ~0.7px by f/4, making vignetting almost a non-issue.
The camera's built-in vignettign correction reduces vignetting to almost non-existent, but you can also correct it in post-processing - set Photoshop's Vignetting correction to +25 at f/2.8 an to +10 at f/4 to reduce vignetting to minimum.
Distortion is average in this lens - at ~1.4% barrel distortion is not going to cause major issues in real life, although in some cases might be visible around corners.