How long can you use an almanac?

Note: this is a reissue of a Nog originally published in 2008.
When you turn on your GPS receiver - what happens? Well, lots of stuff.  But primarily, GPS receivers work in a two stage process:

1. Look for available satellites to track
2. Do everything else

In this article, I want to focus on step 1, we'll get to step 2 later.  This is probably common knowledge, but for the record I want to state it.  The GPS receiver uses an almanac downloaded from a single GPS satellite to help it determine what satellites are above the horizon as it searches for signals.  Makes sense to not look for satellite signals that aren't even visible - it decreases your time to first fix (TTFF).  Since the receiver is simply determining whether a satellite is above the horizon, the almanacs don't have to be very accurate.  They are typically a coarser version of the precise ephemeris broadcast by each individual satellite. 
What I do want to discuss is how long you can use an almanac for analysis.  Your receiver will usually download a new almanac when it sees that a new one is available, so it always has the freshest data.  When you do analysis though, sometimes you may not have the latest almanac (or the one correct for the time of analysis - a related problem).  So, is it ok to use any old almanac for analysis?  Since they are not the most accurate ephemeris representations, should I be using them for analysis anyway?  I'll answer these questions and show some interesting graphics that bring the point home.