Perhaps a freemium model would make sense to some: for $5/month or $50/year, make all your answers invisible to the soulless and unforgiving collapse-mods, allowing them to sink or swim based solely on the popular up/down votes.
Alternately, rather than a monthly fee Quora could allow users to bolster their natural vote-strength by "putting their money where their mouth is" – say, adding 5 additional votes for $1 per answer.
Along similar lines, making the "ask to answer" feature available for a one time fee, or exclusively to premium members might bring in a bit of cash without too many complaints, especially if a decent cut is given to those who are being asked to answer.
Finally, paid "featured question" spots in feeds that remain 'sticky until clicked/X overall impressions', rather than simply being washed away in the standard stream, would help get exposure for questions that people feel are urgent/important enough to pay for, so long as it was done tastefully/affordably.
If Quora was to charge a monthly fee, what is the most users would be willing to pay?