That's about what I would expect. The two major weaknesses of "naively" training a Go player in this no-look-ahead purely-supervised way are:

1) The training data only consists of positions that occurred in professional games. This means positions that are not likely to occur in that context have no training data, making the network liable to play poorly.

2) The lack of any kind of planning ahead means situations that require carefully working out future sequences of moves are not handled well.

However, even in those difficult situations the network is still usually able to play passably showing that there is at least some generalization.

This is quite exciting. I'd imagine combining the supervised version with the usual Monte Carlo search would result in a huge jump in strength, and that doesn't seem too difficult of a task to do. Normally the Monte Carlo bot has a strong fighting ability, but about 0 knowledge of fuseki. This one seems to have mid-high level dan in fuseki, and yet if you get a ladder, you win the game.

Since this neural net is trained to respond as a professional would to a given board state - could it be that a 'naive' or less sophisticated level of play would elucidate a matching level of response ?

Concretely, if the player plays worse does the net respond at that level ?

Thanks for catching that, I fixed the link.

The network itself has no capability to pass its turn, which is a consequence of the fact it was only trained to predict player moves, not passes (we thought trying to learn when to pass would be difficult and a complication best avoided). So essentially you have to play until it seems clear to you the position is won or lost. If you played on indefinitely the DCNN would start playing terrible/suicidal moves rather then passing, so you could beat in the long run.

But it doesn't seem possible on the web link for the player to pass and then see the score?

No, you'll have to estimate or count manually, as it stands. An "end game now" button sounds like a reasonable fix, though.