Like many others, this novel will capture your interest to start, then slowly taper off, and you'll finish it more out of obligation to it's beginning than for the words themselves.
This is Monsieur Poseur's book report, kiddos! Strap in.
The book is very human; most of it's power isn't from the rigorously thought out scenarios (a math degree must be good for something) but from the mostly believable characters. But over time, the story becomes less and less focused, more reliant on MacGuffins and cheaper tricks. There wasn't a part of the story I specifically didn't agree with, but it got boring towards the end no matter how many rabbits the guy pulled from his hat. You can think of it like a Beetle full of American tourists going through Europe, driven by an overenthusiastic host, with less than enthusiastic passengers. And the ending kinda sucks, mainly because it's nowhere near an ending.
Teela Brown's luck, or the success pattern inherent in the human race or whatever, is used liberally to cover up the holes in the plot from the beginning. It's less of a moral or character trait of Teela's, than it is a defining characteristic of the story itself: Everything was governed by Teela Brown's luck. I shouldn't have to explain why this is stupid and somewhat creepy when 'Louis' talks about it. The last parts of the book seem to be more for 'Louis' (*ahem*) than for the reader, where strong ideas are thrown out there in a last ditch effort to resolve the countless interesting conflicts that the beginning made. 'Louis' is not a good peacemaker, for a diplomat.
While 'Ringworld' certainly is aware of the tropes that plague novels, it can't escape them itself. Making us more aware of them is one thing it does do well.