This is a follow up on T52021 which was more specific to Branched Path Tracing and which ended up partly addressing some issues with transparency as well. This new task is specific to the handling of transparency, as requested by @Sergey Sharybin (sergey) and detailed below.

These tests used a nightly build of Blender, version 2.78.5 1bd9531fda7.

The example starts off with some text rendering with an opacity of 0.3, and the outcome looks plausible:

But bringing the opacity all the way down to zero shows the issue:

Taking these phantom shadows and artifacts and blending over the original scene shows the exact positions of the artifacts:

Here is the blend file for the scene: