Well to be honest I find this a help not a hindrance!
I haven't learned much Korean so I didn't know that word (thanks though) but to my mind this is just three ways of saying the same word, and each way is specific to its own language. I mean, you couldn't accuse the Korean word of sounding Japanese, and you wouldn't really suspect that the Japanese word was Chinese (this assumes you have a bit of experience of the sounds of those languages). So for me I would pretty much be remembering "toshokan図書館", because that's the first one I learned, then I add to that "túshūguǎn图书馆" which I actually just learned yesterday. First I remember ka- goes to gua-. Then I add the tones. I can remember the first two as a pair because it's the same contour as toshO (pronounced with an English accent, which you don't do, but which is obvious for me to remember). Add the last tone, and you're there. Total time, 3-10 seconds?
But if I had to learn "library", "toshokan", "kirjasto" (Finnish, sorry, I just got that from Google translate, hope it's right

), then wouldn't it be harder?
I think that all of what you are saying is correct: that in some ways it seems confusing to have similarities, and in some ways it makes life easier.
Let's exaggerate the situation though, and see what it looks like. What if you had more than three languages that were slightly similar?
French: bibliothèque
Spanish/Portuguese/Italian: biblioteca
Dutch: bibliotheek
Danish/Norwegian: bibliotek
Swedish: biblioteket
I'm going to be radical and say
this is the same word but with a different pronunciation.
OK let's say I have to learn all these now. First of all, I think they have in common "bibliotek". French words never end like that so obviously it's -thèque. Italian, Spanish, Portuguese don't end in -ek so it is credible that they all go to -eca (I say "credible", i.e. it can be easily retained in my mind without any great leap). It makes sense that Dutch would be -theek. Then I have to remember the Swedish one as an exception. I know a bit of Norwegian but not Swedish so all I can relate it to is that when Norwegian words end with -et it's the same as saying "the ...", so I just pretend that that's the reason for it in Swedish (it isn't, but I don't know that until I study Swedish a bit more).
In the cases where I have knowledge of the language, I can translate/transmute it into the style of each language. In cases where I don't know the style of the language I have to relate it to something I do know. In any case, I think I know all the words now. I'm going to write it from memory now: French bibliotheque, Sp, Po, It biblioteca, Dutch bibliotheek, No, Dan bibliotek, Swe, biblioteket. Left out the accent on the first one to save time finding it on the keyboard (I'm not looking at the screen). Got a bit tired at the end and spelled the Swedish one wrong then corrected it. By a freak I got them in the right order!
I can do that because: I see the countries on a map in my mind and for most of the countries I know how "bibliotek" will be pronounced/spelled; when I don't know I relate it to something I do know by some simple process that may be wrong but which is vivid. That's exactly how we do it with the RTK stories.
So, to go back to the topic, it should be the same for remembering several "styles" of writing what I would call the same character. If I can read characters at all, it's easier. If I've had a lot of experience, it is a lot easier. If they are similar, then it is easy (they have a "local pronunciation"*) - for example I can recognise the primitive "言" in traditional and simplified system (語->语) so, with that knowledge, these two are the same character but "pronounced differently"*, i.e. the style changes when you go to mainland China. [*
NB of course here I don't mean pronunciation in a literal sense, I just mean a local style of writing the same thing, just like I suggested a "local style" of making a similar sound earlier on in this reply]
Even if there is a "radical" change (sorry, making a pun >< ) like あ is derived from 安, you can see that,
given the local rules/rules of style, if you can see how the two are related then you can remember them both.
In conclusion, as soon as you know one (character, language), you can start to remember variations of it. But it's sometimes a long way to go to learn the first one. Until then, we can only relate it to something we do know. The sooner the better!
Apologies for any language errors in this reply
Edited: 2011-09-22, 1:16 am