Well, all depends.  I've been a collector (normal coinage) for probably 20+ years, and if I see a decent close up shot of a coin I can usually guesstimate grade within 1-2 points with a 10 second look at the photo.  And that's just as a hobbyist.  Imagine if you're a professional grader and all you do day in and day out is look at coins.  They've probably each seen 90% of all coin types and conditions ever graded, and can easily peg a coin with 95% certainty what it would be very quickly just by picking it up before it goes under the loupe.

Now, there's exceptions to the rule as well.  I'd guesstimate that at least 85% of the coins going through a TPG are "common" - Morgan/Peace/Ike dollars, ASE's, all general US Mint coinage from the past 100 years.  Those I would say a pro grader could pick a spot-on grade in probably under 5 seconds since they see them all the time.  The "uncommon" ones - and those that are high value of any series - are usually flagged and go to a special panel of graders who spend much more time examining them and this time they all talk and come to a consensus on what it is.  Now, we're talking coins that are worth many thousands of dollars here... anything we're talking about with our rounds and most modern mint issues are not anywhere near that.

And the reason why its so quick is that they're looking at certain areas of the coins, not the whole thing.  Certain areas of the coin count towards the grade, others not so much.

Each series of coin has a set of "focal points" where your eyes naturally tend towards when you look at it.  This is what the graders concentrate on, and the grade is 99% of the time derived from.  It's easy and quick to examine the focal points of most coinage when you know them.  I can look at an eisenhower dollar and in under 10 seconds usually come within a point of a professional grader.  They don't examine the parts of the coin that "don't matter", such as the edge, and ignore most rim dings.  Especially in our case there's usually a hologram covering a good chunk of the reverse, which is mostly ignored unless it's mangled.

You're not too far off tho with your comment about the "bad day", graders are human after all, and they will get it wrong enough.  I'm sure there's more than a few coins in a 69 slab out there that should have been 70's, which is why 70's are held with such a higher premium.  It's so hard to get everyone to agree that a coins is that good to deserve it.