I saw RotK five times... and only one of those times was with a hardcore Lord of the Rings fan.
However, my worst (worst still being awesome, but out of all of the times I went this one was insane) experience was when I went with a friend who had seen the movies and was obsessed but didn't really know what was going on and made loud comments every time Orlando Bloom was even on the screen, clung to me during Shelob, and asked me questions every 5 seconds and then made jokes during the Grey Havens while I sobbed... they also informed me that "my man" was onscreen everytime Viggo did anything, because one time I made an offhand comment (ok I was drooling a bit) that Viggo was quite attractive....
Anyhow.. it was a bit insane but still fun, at least she wasn't criticising it, she was just.. overly enthusiatic...