When it comes to game-breaking glitches, I only experienced two.
1) Camera was completely stuck during the Castlemark Dungeon (Which is a terrible dungeon on its own). I could not control the camera at all, and was stuck in a position where it made any kind of exploration impossible. I could not even activate stuff because the screen would not allow for the prompt to appear. Had to go back out of the dungeon, go into a battle and issue a command to one of my allies to fix this.
2)
Chapter 7 I believe.
When it comes to graphical glitches, one time during the very early morning, the lighting was fucked up (Shadows and every object and characters in them looked all black, like burned). This got fixed by itself and never saw it again during my playtime.
I think that's all I experienced.
EDIT: Oh yeah, also Gladio turned almost invisible twice during my game. Entering a cutscene fixed it.
1) Camera was completely stuck during the Castlemark Dungeon (Which is a terrible dungeon on its own). I could not control the camera at all, and was stuck in a position where it made any kind of exploration impossible. I could not even activate stuff because the screen would not allow for the prompt to appear. Had to go back out of the dungeon, go into a battle and issue a command to one of my allies to fix this.
2)
In the Water ruins in the Vesperwood,
An Iron Giant is supposed to destroy a bridge, which won't regenerate itself until you win the battle. Well, the battle never initiated and the Iron Giant never fell down with me (It disappeared completely). So the game refused to fix the bridge. In my frustration I reloaded my previous save, losing half an hour of gameplay. This fixed the issue, at least, since I could fight the Iron Giant on my second attempt.
When it comes to graphical glitches, one time during the very early morning, the lighting was fucked up (Shadows and every object and characters in them looked all black, like burned). This got fixed by itself and never saw it again during my playtime.
I think that's all I experienced.
EDIT: Oh yeah, also Gladio turned almost invisible twice during my game. Entering a cutscene fixed it.