Information about Shinigami's Powers
While vaguely described in canon and never in reference to Shinigami's own abilities, certain characters in Soul Eater possess the ability to see the souls of the living. Stein--one of the strongest humans in the series--is capable of determining personal characteristics concerning another person by a simply glance at their soul.
Since Shinigami is many, many, many times more powerful and experienced than Stein, it can be assumed that his own version of the ability is far more powerful and accurate. Atop that, Shinigami constantly produces lists of sinners around the world (generally people who have committed murder repeatedly) despite being locked away in his home of Death City. It can be assumed that his power to perceive souls expands the globe to an extent, allowing him to judge people as good or evil.
Think of him as a Santa. A Santa who...gives coal that actually kills you.
The actual appearance one's soul differs between individuals. The appearance generally takes prominent physical features of a character and displays them on a giant, clear orb. Sometimes the appearance of the soul is determined by unique qualities of the character, right down to their fighting style: the character Mifune often incorporates police tape with the words "KEEP OUT" plastered on it and his soul is covered with enormous versions of this tape.
Many times souls will have a face on them that represents what would be the character's default expression. Tsubaki has a sweet, innocent smile, Black*Star has a huge grin, and things like that.
Most importantly: Shinigami will be able to judge characters. This ranges from being able to tell that Laharl is actually a troubled boy who is good deep down to being able to tell that Teatime is a murderer. Powerful characters--most prominently Aizen--will be able to naturally obscure his ability to judge them; he'll learn that Aizen is sketchier than he lets on and should have an eye kept on him, but won't know the extent of his evilness.
In a way, Shinigami's soul perceive can be seen as a form of empathy, as he can accurately judge emotions quite well. A character as reclusive and bottled up as Soren would appear to be a very hurt and scared individual.
Go ahead and comment here if you'd like Shinigami to be able to look at and judge your characters' souls. You can be creative and give a little description of just what their souls look like. Since I obviously don't know every single character intimately, a short description (seriously ONE SENTENCE would work best) of the characters' genuine, actual, deep-down personality would be good.