I found this nifty Periodic Table in Esperanto online. You can view it here. (Cp still lists the generic name Ununbio, and Francio is given as the name of the element Francium, instead of Franciumo. Other than those two errors, I think it looks alright.)

I think a poster-sized Periodic Table in Esperanto would be cool to hang on a wall, but I doubt if such a thing exists.

This periodic table is mojosa! I found another little error: the "Posttransition metals" are not translated.
By the way: You can order a printed version of the table, but just in english. I asked whether an esperanto version might also be available.

Here is the periodic table in Esperanto:

Perioda Sistemo

Why not give the elements at least semi-logical names pertaining to their qualities like in German and Japanese? It just seems pretty pointless otherwise.

We used to do that (Kloro=Green, Hidrogeno=Water producing) until chemists find that some "qualities" are actually shared by large number of elements. Is "oksigeno" the only element that produces Acid? Or is (in Japanese) nitrogeno the only element that suffocates? Even worse, sometimes these descriptions are wrong! Nowadays who dare to declare Azoto "lifeless" should go and see how much N-fertilizer our farmers use.

If we are talking about what facilitate memory, I think knowing "Polium" is named by Madam Curie in memory of her motherland helps a lot to memorize it. Kaj simile plu.

They why not have the name be of it's distinguishing feature and add -um?

@gyrus
What I meant in my last post: there are very few distinguishing features, and most likely not enough for 118 elements!

"Water producing" doesn't distinguish H from O.
"Acid producing" doesn't distinguish O from H, especially nowadays when we talk about "acid" most will think of H+.
"Suffocating" doesn't distinguish N from, say, helium (and all the gas except O2)

get what I mean? For example, how will you name "P" in this fashion. Or even tougher, Ru? And there is the problem about the syllable-economy which I will address below.
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However, I have something else in mind that I want to point out about current names of elements.

1. I hope Eo names for elements can match their symbols. I know this is not always possible with some letters not existent in Eo (Y, W, Xe) or those aren't pronounced the same (C, Ca). And that's OK. However, when choosing the name for some elements with different naming in multiple languages, we should pick the one closest to the Latin symbol.
(Ekz: For "N", Azoto should be replaced by Nitrogeno. Can someone please edit this wiki page.)

2. Though I don't think the symbols themselves should be analytical, I do think the naming system for molecules should. The ideal will be that when we see the name of a molecule we instantly know how its formula is.

3. For convenience of use. I have noticed that some of the names of the elements may actually be too long to be handy. Especially so when we consider the frequency of use of those element!
My ideal: the higher the frequency, the shorter the element's name should be.

So what are the elements that appear in the greatest number of molecules? Organic chemistry gives us the answer: C, H, O, N (and the lesser: Na, Mg, K, Ca, P, S, Cl).

Now,
Karbon- (2 syllables)
Hidrogen- (3
Oksigen- (3
Nitrogen- (3
Short? Not for me. (In Chinese the names for all elements are Monosyllabic) And in fact, I can see that neither are they short enough for some of our Esperantist chemists. See entry in ReVo hidrokarbido, oksido, nitrido.
(FYI, -ido here unofficially means "combination with", so we have words like Klorido, Jodido, etc)

Therefore, I, with the interest of chemistry Esperanta at heart, propose the following alternatives to names of elements:
H - Hidro
O - Okso *
N - Nitro
* I know it's homonym with an already existent word. But I think the same can be said about "oksido", and, personally, I never like this "Okso"=ox, which by standard of Bonlingvism should simply be vir·bov·o. (source)

LyzTyphone:In Chinese the names for all elements are Monosyllabic

Wow, I was expecting words with two or three characters. I looked at Chinese Wikipedia, and I think it's quite amazing that Chinese has specific characters for rhenium, praseodymium or roentgenium (which was discovered a few years ago).

I like the short names, I'm not in favour of just changing words but shortenings like that seem to always be understood easily.

LyzTyphone:(Ekz: For "N", Azoto should be replaced by Nitrogeno. Can someone please edit this wiki page.)

There are at least three elements which don't match up with the Latin-derived symbols, because of their Fundamental names: antimono, oro, and azoto. That means that whatever other synonyms (stibiumo?, aŭrumo?, nitrogeno) become part of the language, they will always remain. There is not one reason why these three exceptions call for a new word. You yourself said that there are some which can't match up because they have non-Esperanto letters, what's wrong with three more?