Looking at other answers, I am confused about the question. Do you want to glitch physics in the game, or in reality, or glitch physics in the game in such a way that it could be done in reality? Do you want to know how to do it in a game? Do you want to have unusual responses to the controls, so the resulting actions are still law-abiding, just unexpected, or do you want the actions to respond to the controls appropriately, just in an exaggerated or diminished fashion?
Every game has 'constants' in it, that are used in algorithms. These constants, for instance, determine the level of play, or the speed of characters, or the level of intelligence. Inserting some random number function (that is itself triggered by a randomized 'do/not do' routine) to randomly alter them at some random point during game play would certainly look like a glitch, but would not change the overall coding of the game. For instance, something might fall slower or faster, fly farther, hit harder, have more or less strength, based on the value of a variable constant. These changes could be temporary, or lasting.
Also, every game has selection structures, where a value of choice determines what consequent code is executed (jump, run, duck, fall, etc, in response to what controller button is pressed). Putting in a random number function for the variable choice that is triggered at some random time would make the game appear to be glitchy and unpredictable, but the coding would actually be intact. Again, these changes could be temporary, or lasting.
You could also do this with the variable that determines what comes next. Usually, this variable is incremented, but if it randomly was randomized, it would certainly look like a glitch. (For instance, sent to a different room than expected, or go in a different direction than expected).
Since everything still follows rules (which can simulate physics), the integrity of the game is not altered, just the implementation.
In a way, it introduces the concept of unpredictability to the game. Things are going peachy-keen, you think you have it mastered, and then...
However, someone who plays the game long enough would be able to discover what glitches and what doesn't, so it would have coherence to them. Eventually this information would hit the internet blogs. It would just become another 'rule of the game'. Thus, the game designer would simply make the probability of the glitches in the random function even less probable, and thus more sporadic. Perhaps some players would never experience them.
In essence, this is what was built in to the 'poker-playing' algorithm that out-played world champion human poker players - the ability to bluff. 'The feat represents a leap forward in developing artificial intelligence that can learn with incomplete information' link - the ability to respond in a way that was not expected or predicted.
But if you want to know if such things are possible in the real world, I would posit that only the first one - being able to change the value of generally-accepted constants would even come close. For instance, a 'bubble' in which the gravitational constant were changed locally, so things fell slower, faster, or not at all. Or that the universal speed limit c was changed in a local bubble, so things could go faster than our expectation of c in that bubble. That is, you are not changing the rules (the math, the equations) that apply to gravity, just the value of the constant. e = mc^2 still applies, just a different c value.
Physics today can't rule this out, we just have no idea what the mechanisms for doing so would be, or even look like, let alone how to implement or manipulate them, to modify the constants. But just because we can't do it today, and have never experienced an event where it was done, with our limited knowledge, doesn't mean it can't be done. My guess? There is absolutely no reason why these constants could not be different in a black hole, or perhaps a worm hole, or even another universe, for instance. We just don't know, and therefore can't answer that question definitively.
