My favorite is in the Dawguard DLC for Skyrim. If you somehow get far enough into the DLC to enter the Soul Cairn and you didn’t do the main story quest where you kill your first dragon, you’ll get unique dialogue with a dragon you meet in the Soul Cairn. He calls you Dovahkiin, and you can ask him why he called you that, to which he responds something like “I do not know, it just felt right to call you Dovahkiin. Perhaps you will learn why soon”
Funny that they thought of that, but then slipped up that you could become archmage before you have to ask the archmage for help. But there’s no dialogue for the quest if you are the archmage. So if you progress in the wrong order, you get stuck in the main quest.
They may have fixed it since, but that was a huge error.