Yes, the order does matter.
As pointed out in this answer , it appeared that at first glance, Chloe can't do math.
The number of gates just appears to be far too few, she states that there is a 1 in 63 billion chance of randomly dialing a particular stargate.
However, given 38 chevrons, and 7 random dials, that gives the number 38!/31!, or 63,606,090,240.
Thus mathematically and given some random facts in episodes, the order must be important.
Note that the 39th one is unique to each site, and thus isn't included in the calculation.
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I have to disagree with Dima - the order of glyphs MUST matter.
My rationale is as follows: We have often seen people having to rush to dial the gate.
They've been taking fire, Jaffa/Wraith/Replicators closing in.
The team has seconds left, and they're trying to dial as quickly as possible.
They dial a few glyphs, then frantically search, hit another glyph, and then quickly punch in 3 more (ending with the Point of Origin), hit the central crystal, and the gate opens.
SG-1 is saved!
It's a scene we see literally dozens of times over the course of SG-1, and at least several times in the Atlantis episodes I've seen.
It would make no sense for people to waste precious time looking for a particular symbol as the 3rd, or 4th, etc, if the order wasn't important.
So, while there's no logical reason, based on Daniel Jackson's original theory of addresses (6 points to define a 3D location, 7th for Point of Origin) for the order to matter, the character's repeated actions demonstrate that it is.
Edit:
Also, in the Atlantis pilot episode(s) "Rising", Ford memorizes the address the Wraith Darts dial, but he didn't memorize the order.
Sheppard and McKay discuss this, and Sheppard explicitly points out that they need the order.
McKay is initially dubious, but points out that knowing the symbols cuts down on the possible combinations.
There's a little humor in Sheppard having already done the math and being ready with the number (6! = 720).
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As far as I remember, the glyphs represent stars, which are endpoints of line segments.
There are 3 pairs of glyphs, to represent 3 lines, whose intersection is your destination point.
(Come to think of it, you only need an intersection of two lines to define a point, but whatever...).
So, in that case, the glyphs must be grouped into pairs to represent the lines, and the point of origin must be last.
But the order of the pairs should not matter.
I suppose that it is simply more convenient to memorize a sequence of 7 glyphs in a particular order, which is why they always dial them in order.
Edit:I did not say the order did not matter at all.
You cannot shuffle the glyphs randomly, but you can shuffle them somewhat.
Let's formalize this.
Let's denote two glyphs defining a line segment as a_i and b_i, and let's denote the point of origin as o. One way to specify a valid gate address would be a1 b1 a2 b2 a3 b3
o
In this case, you should be able to swap corresponding a and b without changing the meaning, or you could swap (a_i b_i) and (a_j b_j) without changing the meaning.
Alternatively, you can use this convention:
a1 a2 a3 b1 b2 b3 o
Here again you should be able to swap corresponding a and b, or you can change the position of a pair.
In other words, a3 a2 a1 b3 b2 b1 o should still be a valid address.
This seems to correspond to @Jeff's observation.
Of course, you can come up with other conventions, but these two make the most sense to me.
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They have to be in order according to the rules of the show, but it's one of the many bits of Stargate canon that makes little sense.
As previously answered, the points should be reversible, and only 4 of them would be necessary to calculate a point.
It should be noted, however, that calculating any specific position within an area of space using only 38 points within the area isn't possible,
only the 63 billion mentioned.
Sure, that sounds like a lot, but compared to the number of possible positions a gate could be in an area the size of our galaxy, it's ineffective.
Adding in the stellar drift, the address system should not be adequate as described. (Though since the gate can identify one end by point of origin and needs the 6-symbol coordinates for the other, and also given the correlative update system mentioned in some of the episodes, it would seem the gates
all know each other's positions anyway, and the address is little more than a simplified way to enter the destination
(basically the naming system mentioned near the end of season 7.)
I suppose it could be seen as a password system, as well.
Of course, given that they calculate planet locations with the gate addresses in some episodes, the science/simple logic comes into play anyway.
Just one of the heap of plot holes in the franchise (and one of the many they've made fun of themselves for, if I remember correctly.)
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The spoken word version of the planet with the ZPM was
Pac La Rush Ta On As At (Paclarush Taonas also means "Lost in Fire" in Ancient.)
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Also, the symbols can be spoken, remember.
I recall that hell planet with the zpm that SG1 needed to power the chair on earth, that they didn't know was there, my episode knowledge is shaky. :)
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Excepting the final glyph for point of origin, does the order of the glyphs matter when dialing a Stargate?  I don't recall ever seeing someone dial an address out of order, or directly commenting on order mattering.  Looking at the design of a DHD, it would seem like it doesn't matter, as there's no indicator on the DHD itself of the order of glyphs.
Does the order of glyphs matter in Stargate addresses?
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The order of the glyphs does matter, and people look for particular symbols in order. The order of glyphs does matter and it is canon even though it makes no sense. Clearly people would not waste time trying to look for specific symbols if the order was not important.
The order of glyphs does matter and it is canon even though it makes no sense. Clearly people would not waste time trying to look for specific symbols if the order was not important.