Broken Game Rules
Broken Game rules can greatly ruin a games experience and can be considered to be a bigger bug/glitch. Rules govern how you play the game, and how you interact with every object but if these rules have unforeseen errors or improper coding, then it can result in some erratic happenings in the game. An example of a broken game rule would be if when you equipped an item you could no longer move your character. Instances like these might be considered not that big of a deal, but other conflicts in game rules can cause a game to crash or freeze.
Screen Tearing
Screen tearing is a fairly common problem and sometimes can barely even be called a glitch. Especially in computer gaming dealing with first person shooters. But, if a game is putting out too much screen tearing regardless of how powerful of a digital output you have, it can become a nuisance. First let me explain what screen tearing looks like, screen tearing appears as uneven or unbalanced images lay horizontally above and below each other. Images in your Xbox 360 game will appear to be split in two or more parts for fractions of a second. These splits can be very subtle and hard to notice by casual Xbox gamers or a person not knowledgeable in the ways of game testing. The in game cause for screen tearing is usually a camera is swiveling too quickly for the frame rate, monitor or output device, but it happens mostly in highly sensitive controls in first person shooters.

A more technical explanation for screen tearing is when the number of images/animations or what can be called a frame rate is too high for an output device like a monitor or TV. When the camera or view moves at such a high rate your Xbox 360 or output device cannot catch up to the amount of images that are being produced in the game. This can be avoided if the game is properly constructed and the correct refresh rate is contained in the output device. This isn't so much of problem that game testers look for because these are things that should be evident to the Xbox 360 game developers. But, as a game tester, you should know this lingo and make sure there is not an overly screen torn Xbox 360 game.
Texture Pop-ins
Texture pop-ins are sometimes experienced in Xbox 360 games, and it happens usually when your character travels in a new space and all the textures on in the game haven't fully loaded yet. The surface will appear blurry until the texture completely loads. This glitch doesn't usually hinder game play in any way but can take away from the overall experience.
Problems with Geometry
Geometry is what forms the world of gaming, it constrains you to a certain playable area and contains its own parameters. Problems with geometry can result in the player going through a wall, getting stuck in a level (physically), or setup faulty gameplay situations. Overall this can be a bigger glitch or problem with a game, these mistakes need to be found and fixed early in the development process. Although, these mistakes can be obtrusively noticeable, they still exist in a lot of games. Sometimes these mistakes can't be found without taking radical steps to fool around with a game. Soon, players can find every little glitch in a game, such as hiding in a wall while shooting opposing players. Developers find this to be a big problem.
Freezing and Crashing
Freezing and crashing may be like a brother to computer gamers but to console/xbox 360 gamers this is an unexpected event that makes even a grown man cry. It should be pretty apparent what crashing and freezing is, it is when the game crashes/turns off abruptly or freezes on one screen. It can be caused by a variety of things, and sometimes it doesn't even involve the game itself. If a game makes enough conflicting decisions the game can crash, it can also be because of software to hardware compatibility. Finally, if too many things happen on the screen at once it can also make for erratic behavior.