I was out for a stroll, heading back to the starting area with my Pet Tiger, Gina. I decided to cut through Sepetrmaru when I noticed this… Apparently my Tiger had an issue with one of the Guards and was locked onto it in a stare down.
I continued to walk and the Tiger followed but was STILL giving the Evil Eye to the Guard.
We soon left the city and were walking through the desert when I noticed that my Tiger was following me while walking backwards, gaze still fixed in the direction of the guard.
I had flashbacks to a Nickleback concert when the real Gina saw a girl wearing a similar top. 
Yeah something is allowing the Tiger to target a non aggressive NPC and it will not loose focus over distance. I had to stop follow and place Tiger to correct.
Other than that the Tiger did well and was fun to play going into a lower level Thrall camps and watching it shred everything!
The only other problem was in it’s behavior during the Boss fight in the Dregs. It would disappear into the acid then pop back up several seconds later unharmed and loose focus on the Boss until the next time it hit me.
All in all it was a lot of fun! 
EDIT
This was in single player with no mods. I found the official servers crafting vs fuel settings to be nearly unplayable for the limited time I am able to play.