Depends how you mean exploit. Not a lawyer, but to a first approximation, doing anything in markets to elicit a response from others rather than for bona fide economic reasons is illegal market manipulation so active exploitation is rarely done at serious firms. It's usually individual day traders or offshore boiler room type groups.

Passive exploitation, as in detecting predictable future actions, is probably common, if unintentional. Most automated traders are searching for anything that predicts an imminent price change, on average. Predicting future actions and predicting prices are roughly equivalent. As you move along the continuum from straightforward arbitrage to esoteric black box quant stuff, it becomes more and more difficult to understand how or why a trade even works. I'm sure there are models that predict prices very well solely because they've locked on to some combination of tells unintentionally leaked by another algo.

Here's an example of someone who built a model to detect algorithmic iceberg orders reloading: https://mechanicalmarkets.wordpress.com/2015/04/30/market-da... - he makes an interesting point that any quant data mining order book event sequences that predict strong price movements would find the same pattern easily.