Ukraine's mistake was being impatient and ignoring the EU-Russia deal to hold new elections by the end of the year. Had that happened and Yanukovych was elected out, then the Russian regions probably wouldn't be up in arms, and Russia wouldn't have much cover.
Russia's mistake was being so heavy-handed with Crimea. As much as I hate Putin, I agree that Crimea should belong with Russia--it was Russian until it was "gifted" (really, just a meaningless administrative shuffle at the time) to Ukraine. But with the extreme propaganda ("neo-Nazis"? Seriously?!), the silencing of opposition media, the troop movement, the election can't possibly be taken seriously. There's a good chance that Crimea would've voted in favor of breaking away anyway without these glaring violations.
Neither side is acting very rationally. They're racing off a cliff because they can't get their f-cking emotions in check.
Keep in mind that Crimea is already an "autonomous" region. It's already quasi-independent. Ukraine's desire to continue its (tenuous) hold is basically the result of pride, nationalism, and (most importantly) fear of Putin (which is not unfounded).