Q:

How to deal with the fact that web apps are always changing? 

Many answers are going to be workarounds.  As web apps improve and solve these issues the workarounds break.   Even official answers may change drastically over short periods of time with some web apps. 
How do we handle this sort of change? 
I know on many Stack Exchange apps, the best answers are timeless, but it seems hard to give timeless answers for web apps. 
Can moderators mark questions as "unanswered" if they notice a solution that previously worked no longer does?   

A:

The best people to spot this sort of thing will be those that encounter a problem that isn't solved by the accepted answer. 
In that case there's a number of things they can do:

Comment on the answer saying it no longer works. 
Down-vote the answer - if they feel really strongly about it. 
Edit the answer - if they have enough rep. 
Edit the question - if they have enough rep. 
Ask a new question, referencing the original explaining why it doesn't work. 
...

Anything else would put too much onus on the moderators to be constantly reviewing questions when they have (presumably) other things to do - like earn a living. 

A:

I guess users with enough reputation could mark the questions as being no longer relevant and pointing out to any potential new answers to the problem. 
Something like this (at the top of the question):

This question is no longer relevant as of 2010/07/20, see below for related questions:

Question 1
Question 2
Question 3

