You don't want to use doors that go inside or outside because those are "loading" doors and they'll take too long, before you realize there is no such thing as loading in real life.
Whenever someone gives you an errand to do like getting some groceries or picking something up, you think "ooh, a side quest!"
You expect people to make random comments about the empire or their families as you walk past them
Similarly, you expect policemen to comment about recent dragon attacks or how long it's been since they've had a good bandit raid.
Whenever you hear about a criminal or gang on the news or whatever, you almost offer to go kill them for money before remembering that would be dangerous and probably illegal.
Skyrim influences your clothing choices, like I once bought these boots because they looked exactly like the vampire boots in the game.
You sort people from real life into Elder Scrolls races.
Battle music starts playing in your head when you see people you don't like.
Every time you persuade someone to do something, or you win an argument, you imagine your speech skill going up a level.
You want to learn lock-picking for real.
You've actually pick-pocketed members of your family and succeeded.
You become interested in medieval history because it's kinda like Skyrim.
That's not an energy drink, that's stamina potion.
Every pretentious jerk you meet is probably a Thalmor agent.
When you buy something in a shop, you wanna see if they'll buy any of your unwanted junk.
You'd totally read someone's journal if they just left it lying around on a table somewhere.
Every time you open a book, you hope one of your skill levels increases.