One little-known feature of the Japanese Input tools on OS X is the ability to easily access a whole lot of unicode symbols without having to go dig through the Character Palette each and every time. If you enable Japanese Input (also known as Kotoeri) on your mac, hitting a keyboard shortcut (apple-space by default, I think) will toggle kana input on and off, whereby you can type japanese words in kanas and press the spacebar to pick a matching kanji (followed by ‘enter’ to validate the transliteration).
The nifty bit comes from the availability of UTF-8 characters that are not kanji, but nonetheless useful in a lot of situations. Just as any other kanji, typing a kana sequence (usually the name of the symbol in Japanese), followed by a press of the spacebar, will automatically let you insert the desired symbol.
Note: Apparently, most of these work equally well on Windows Japanese Input system, but I haven’t tested it.

For example, any Japanese girl knows all too well how to obtain the following cutesy icons:
おんぷ[onpu]　→　♬♩♪♫
ほし[hoshi]　→　☆★

On a more pragmatic note, you can also choose from a very complete set of arrows:
やじるし[yajirushi]　→　↑↓☝⇔ etc.

And one of my personal favourite: european currency symbols that would otherwise take half an hour to find on a standard US keyboard:
ゆーろ[yuro] →　€
ぽんど[pondo] →　£

Another very cool set for your scientific paper-writing needs:
すうがく[suugaku]／えんざん[enzan]　→　√∃∀≠±∇

Not to mention the entire greek alphabet:
あるふぁ[arufa]　α
べーた[be-ta]　β
がんま[ganma]　γ
でるた[deruta]　δ
しぐま[siguma]　σ

etc. etc.

You will find even more of these in this large (albeit probably not exhaustive) list of special character shortcuts.