Here is the list of all of the known glitches in XY versions so far. If you have one to add, please PM a moderator of this section (with proof) and we will add it to the list.
1. Lumiose City Save Glitch
Occasionally saving outside in Lumiose City can cause your save to be unable to be loaded properly if you turn the game off and restart it. It is thought to be caused by too many things attempting to be loaded at once since the city is so large. Saving inside of buildings (such as the Pokemon Center) appears to be safe, and if you do accidentally save outside and your save is frozen, some people have said mashing the Home button as you try to load or taking out the SD card can possibly unfreeze your save. For more information you can look here.
This is a map detailing where the glitch occurs, released by GameFreak. Don't save anywhere in blue.