Interesting. I can't speak for the smaller boards, but I played on 19x19 and crushed it easily. A quick overview:
As expected the AI is strong at counting and is pre-programmed with a lot of joseki. In terms of reading power it's not bad. As far as issues go, there are a few. It has no idea how to follow-up joseki, it gets confused in the early middlegame and prefers two-point jumps on the 3rd line to more productive moves, it has an overconfident sense of safety when relatively weak groups are being approached. It doesn't quite seem to get sente/gote and will play lukewarm gote moves at strange times. It's also weak at choosing proper joseki.
It has a nasty habit of approaching hoshi stones high.
Here's a quick example of some of my comments:
- Click Here To Show Diagram Code
[go]$$B
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . W X X . . . . X . . . . . . . . . . |
$$ | . . W , X . . . . , . . . . . , . . . |
$$ | . W . . . . . . . . . . . . . . . . . |
$$ | . . . W . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . b . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 5 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 1 . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . 3 . O . . . . . , . . . . . , . . . |
$$ | . a 4 . . 2 . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
I was Black in the game, and some time after the UL joseki was played out, I approached at

. The AI did not pincer, and instead played out this peaceful joseki, which was clearly in my favor. Within a few moves White played
a with no provocation, which I naturally answered at
b. Later White took gote and I attacked his marked stones and ended up killing them. He could have defended a few times, but didn't seem to understand the danger.
On the other hand, later in the game White was attempting to build two small moyos simultaneously. When I played a reducing move at the border of both, instead of trying to patch them up, he fenced me in and attacked. That's one aspect of this AI that I really liked.
So that's it. My quick review of COSUMI. Enjoy.

Edit: It also seems to think two-space extensions are invulnerable. In one game it made two while I was building walls. I thought they looked lonely and urged them to meet one another in the center...