If you want obsessive nitpicking, try tromboneforum.org. We can obsess about mouthpiece diameters down to hundredths of millimeters and percentages of copper and zinc in our horns.
Every group tends to be more critical of those things they love. They really do nitpick because they care. To use a musical example, the Indiana Jones soundtrack collection has some reviews on Amazon that tell people exactly what parts of the scores are missing and where certain snippets can be found. They love the music of the series, so they want all of it to be available. That's the same attention to detail that Trekkers have for plot inconsistencies and logic errors. We all want our favorite things to be perfect, but very few of them can meet those high standards.
Truthfully, I think a lot of the nitpicking began when people wanted to write their own fan fiction and were trying to figure out how all the technology worked so they could write the story as best they could. I can tell you that during ENT, the nitpicking on the Internet was pure blood and guts because we were trying like hell to help those writers produce a good story. But now, heck, it's just pure fun.
I highly doubt that. The fact is that other fiction has plenty of holes and inconsistancies, its just that when you don't care about something, you won't notice. The only reason we notice all the holes and inconsistancies in Trek is because we nitpick - and we do that because we love Star Trek, and when we watch it (especially if its for the 5th time) we pay such close attention that of course we're going to notice little (or big) hiccups. There, how's that for a roundabout way of answering the OP?