At first, I thought we say "see a movie" like 映画を見る
But then I learned of 観る。
Likewise, I learned 探す、 but then I came across 捜す。
I thought 分かる was so clear cut, but my little world is crashing down around me now that I have seen 判る and 解る。

These words apparently have the same meaning, but I'm sure there are subtle differences. I would like to understand these differences so I can be sure of when its most appropriate to use each one.

And I would also like to learn more words that have variations like these, so I won't be startled when I encounter them in the wild.

A little help, please?

If you type any of these words into the MS IME and just rest your cursor for a while, a disambiguation bubble will pop up to explain finer nuances of each word.

Really? I didn't know that
But alas, I'm using the google ime.
Anyways, I'm not sure my Japanese is even good enough to understand such an explanation, if I were to see it.

Ah, yes, homophonic synonyms. There's a whole bunch of them here.
http://www.ss.iij4u.or.jp/~ana/doukuniji.htm

Holy crap, that's a lot of them!
同訓異字 eh? Good to know they've at least got a word for it!

This book deals with this exact issue:

漢字で意味が変わる ビミョ~な日本語

http://www.amazon.co.jp/漢字で意味が変わる-ビミョ%7E...246&sr=8-1

I guess just go for what you see a lot (I've got such a RTK/AJATT attitude nowadays, don't I)

cmtcmt Wrote:This book deals with this exact issue:

漢字で意味が変わる ビミョ~な日本語

http://www.amazon.co.jp/漢字で意味が変わる-ビミョ%7E...246&sr=8-1

I also highly recommend that book. It's made for Japanese people though, so it's probably best for intermediate+ Japanese learners.

My usual guideline is that if the Koujien does not distinguish the kanji usage, most native speakers wouldn't know the difference and I don't bother with it. In the Windows IME you can look for the 一般的 to show you what the normal kanji is. You definitely don't want to be using kanji that even most native speakers wouldn't be able to read (like a lot of the ones in that link above).

Also note that there is considerable difference even among Japanese people -- I've seen 早い used for "fast" rather than "early" in published books and other sources, too consistently to be a simple typo.