The medium form answer is look at the periodic table. There's block of s (which don't count because other than H/He they are buried deep in the atom) and a block of d where the full ones do have ridiculous low melting points compared to neighbors (like Zinc, Cadmium, Mercury...) and a block of p shell where the full p shells are the well known noble gases which are liquid at really low temps and the block of f weirdos who don't matter.
As for the f weirdos not mattering look at the electron configuration for something like Tb. Yes very nice that it has a peculiar collection of 4 level f shaped orbital electrons but I guess the more influential effect is the 5 level s and 5 level p and more importantly the 6 level s way out there in front of the mere 4 level f. Its kind of like D+D or pathfinder multiclass, oh, you have 2 levels of bard multiclassed into your level 10 sorcerer, well whatever, that bard isn't going to matter very much compared to the sorcerer level powers.
So back to your question, the filled p make great gasses at room temp not mere liquids you are totally correct here, the filled d have really low melting points for metals like Hg being a liquid as discussed, and the filled f are weirdos who fool around with electron configurations at mere level 4 when the real chemical action is at level 6 so they don't matter (sorta)
For a more correct, longer form answer someone else will have to step in.
n = Principle Atomic Number ~ energy,size of orbital
l = Total Angular Momentum Number ~ abs(ang m.)^2
n is 1,2,3,...
l is 0,1,2,... (0=S 1=P 2=D 3=F ...)
l < n
Increasing n only (going down a column) increases energy
What does the inequality (and the intuition behind the inequality) tell us about these blocks? Let's go one by one
S block. l=0. 0<n. n>=1. S orbitals have "size 1" or larger
P block. l=1. 1<n. n>=2. P orbitals have "size 2" or larger
D block. l=2. 2<n. n>=3. D orbitals have "size 3" or larger
F block. l=3. 3<n. n>=4. F orbitals have "size 4" or larger
OK, now we jump to the F block. We know the first f orbital we see has size 4 -- it is the outermost orbital of Lanthanum. But what is the preceding orbital, the one with slightly less energy (slightly more tightly bound to the nucleus)? It's the outermost orbital of Barium, and it's an S orbital of size 6.
S orbital of size 6 is bigger than a P orbital of size 4 :-)
This is counterintuitive because it breaks the "bigger orbitals have more energy / are less tightly bound" rule. The solution to the paradox is that the part of the orbital (probability density function) that contributes most to the energy is the part near the nucleus where the electron is far down the rabbit hole, so to speak. While the outermost part of 4f is smaller than that of 6s, the inner part of the 4f has pulled away from the nucleus while the 6s still sits squarely on top of it. 6s gets out to play with other atoms more than 4f but in terms of energy it more than balances that out by spending time really close to the nucleus.
Hope this helps!
EDIT: fixed an off by one bug on the inequalities
But interestingly there is one other element which is liquid at STP: Bromine. Every element has a melting point, and some element has to have the lowest. If Earth was just a few dozen degrees cooler, we'd have no liquid elements at "STP", a few dozen degrees warmer, and we'd have several liquid elements. So there's nothing particularly special about mercury being the only liquid metal.
Check out this periodic table annotated with melting temperatures. See a pattern? You might argue that the other elements in mercury's column have significantly lower melting points than the metals to the left; indeed Zinc and Cadmium have filled s orbitals as well.
But putting general pattern-ology aside, the macroscopic properties of an atom are essentially completely defined by the orbital structure. Observable properties such as melting point depend on these details in a highly nontrivial way.
 Actually many elements are gaseous at STP and have very low "melting" points. Most would actually sublimate at standard pressure.
I think the true explanation is the one you give: STP is totally arbitrary and it's a coincidence that this is the standard we use. That is, my question was a silly one; I didn't notice that this is a coincidence.
However, I think there's a related, more well-formed question:
Br, Hg, and Ga are liquids (or nearly so) at reasonable Earth temperatures (from your , Cs is also), but all other elements seem to be solid or gas at reasonable Earth temperatures at 1 atm.
Why is the range where you get a liquid so narrow?
Why do melting temperatures vary so widely?
What sets the scale, and how does it vary over 4 decades (or three decades, excluding H and He---I understand that quantum effects are dominant there at standard pressure)?
EDIT: Would copernicium be a liquid, if its nucleus lived long enough?
The detailed set of rules that give these results is called quantum mechanics. We have a pretty good idea of the general equation to describe an atomic system (although it's still just an approximation), but we actually don't have closed-form mathematical solutions for many-body systems. The best we can do (except for case of hydrogen, and maybe helium) is to make a numerical simulation, which is what the authors in the article did.
You see, if you throw in even one different electronic orbit, you're liable to radically change the results. If the ingredients are complicated (hundreds of relativistic+quantum-mechanical particles), you're going to get complicated results! By way of analogy, consider how genes encode lifeforms: flip a few CGAT bits and you get cancer; flip some other bits and maybe you'd get some disease resistance.
As to your point about the range of variation -- this is perhaps one of my favorite reasons to study physics! To paraphrase JD Jackson, "Coulomb's law is experimentally known to hold for over 25 orders of magnitude in length scale!" But consider this; the masses involved in the periodic table cover two decades; does this perturb you? The wavelengths of light emitted by a star cover many of orders of magnitude; is that a problem?
(posting as alt because I left noprocrast on)
It would be interesting to see it tipped over as a 3-D bar graph (in K). Some of the rows have little dips in them (not just mercury), not just a hump (with carbon at the peak)
Oh (via few seconds google) http://www.webelements.com/_media/periodicity/tables/cylinde...
(posting as alt because I left noprocrast on!)
There is at least one short story (the title escapes me) that suggests that our #1 tourist attraction for visiting aliens would be total solar eclipses.
edit: Found it, maybe. This does not sound like the one I read.
> Illegal Alien, by Robert J. Sawyer (1997). An alien visits Earth, supposedly for "research purposes", and observes a total solar eclipse. He then speculates that Earth may be the only planet in the entire Universe whose moon covers its sun perfectly (with only transits or occultations occurring on other planets).
One of them orbits just below the other and they happen to be in such a position, that as they approach each other, the lower one gains momentum from the mutual gravitational attraction, while the higher one loses momentum. So every four (earth) years, they swap orbits!
When I first heard about that, I just thought it was awesome :-D
And gas giants don't have a fixed surface you can stand on. I guess you could find the optimal distance to hover in your space ship to see an eclipse, assuming it is above the cloud layer. But where is the novelty in that?
Plus the sun is much less impressive way out there. Jupiter is 5 times further (Sun appears 0.04 the size). Saturn is 9.5 AU and so the Sun appears 0.011 the size.
Eclipses are still not likely just because you have a bunch of moons. Usually moons will orbit on the planet's plane of orbit. The Earth-Moon system (being more of a binary planet relationship) orbits on the solar plane instead of around the Earth's tilted equator, meaning the Sun/Moon/Earth is vastly more likely to be in alignment for an eclipse.
The different organizations have different exact definitions.
I assume they did all sorts of approximate models for mercury. An analytic, rigorous solution must be impossible.
Does this mean that as mercury is cooled to absolute zero, the electron will slow down and mercury will become lighter?
Also, I'm guessing what they mean by "electron speed" is actually electron energy.
> under relativity fast things are heavier
> electrons are fast, they actually have about a 23% weight boost
> heavier electrons 'orbit' closer to the nucleus
> the atomic size is then smaller than anticipated
> this has a bunch of interesting effects on melting points, reactivity, colour/reflectivity etc, (especially of transition metals?)
> this stuff has not always been well understood.