A really good artificial chess player will be almost indistinguishable from a human player. However, the last time I wrote an artificial chess player (as a student project), it showed tell-tale signs: repetitiveness, predictability, and of course occasionally stupid moves when no heuristic was available.
In general, I think that artificial chess players will be more likely to repeat moves when faced with the same situation, whereas human players are more wont to "try something new". But that only holds for fairly simple artificial chess players, and the play style of individual humans.
It is an interesting question. You could, of course, try some standard classification approaches (like SVMs, random forests, Bayesian models, etc.), all that is needed is a good underlying feature representation. You could measure some things like blunder frequency, type of blunders, moving speed (if available), how much emphasis a player gives on solid pawn structures, pawn breaks, dynamic play / tactics, king safety, closed / open positions, open files, material imbalance, sacrificial play, etc.
Naturally, when people think of chess engines, they only think of the good ones (as that is the point, after all, making good chess engines) - but - hypothetically - we could also make some weak or randomized engines. Also, it would be possible to employ different AI methodologies for chess play with a specific intent of mimicking human play.
I play chess myself and I'd like to see more research done in this field, I see that it has been neglected lately, as there is no market incentive to proceed with it now that we have Rybkas and others.
Of course, detecting computer-aided play in cheating detection is often done on online chess servers (like chess.com), though they keep their methods a secret. I suspect it is mostly blunder-check and the time you take to make a move.
I cannot solve your problem, but I can propose you an heuristic in two games.
Play once against your adversary.
First, if you win, your adversary is an human.
If you loose, play again with a chess book. You choose one of the less known opening, for example Desprez opening (H2H4).
If your adversary does not know it, he is an human.
If your adversary know it, he is a master or a computer.
In both case, don't play money.
To conclude, if you want to detect computer, try to play rare openings. Most of the human players do not know them. A computer will take advantage of this knowledge to get a good position.
I just propose a first heuristic based on a simple postulate:
most of humans do not all the openings, all the computers know all the openings.
A cheat detector can use this postulate. It is not sufficient because you can have false positives (very good players), but it seems correct because all the computers will be detected.
When you said incorrect, you thought about the postulate or the heuristic ?
Computer (strictly saying chess engine) often plays very "cold-blooded" variations. If computer has two possibilities: a long win in a calm variation or a rather quick finish in a very sharp one, it will always choose a sharp continuation.
Second difference - computer often plays moves that human would never consider. I call these moves "non-human". For example - a position taken from game Rajlich - Hou Yifan after white's 18th move:
Now chess engines suggest that the best move for black is 18. ... g5! It's a totally "non-human" continuation! Hou Yifan choose a "human" move 18. ... h6.
Third difference is already clearly explained by Azlan Iqbal.
Generally, computer almost never play "Tal-like" chess (romantic, with many sacrifices and unpredictable positions) and would like to finish a game in "Fischer-like" style (quickly, even if a variation seems to be risky for human), not in "Karpov style".
Imagine a special version of the Turing test. In this version human plays chess against an unknown opponent (human or computer). Suppose that this human is a world class grandmaster and his opponent can be either grandmaster or chess engine (playing at the top level).
How do you think - will a chess engine pass the test? Or maybe a grandmaster will without any doubt unmask a ,,silicon" opponent? In my opinion it would be rather easy to unmask a chess engine.