[Babcock_Hall]

Structures 2 and 3 look identical to me.

[Dan]

Got this. Seems that the enolates are same only turned on other sides, or maybe resonance forms. Is it okay?

Essentially yes. Though you have now switched to enols instead of enolates, but conceptually you are there. As has been said, the two enols you drew are identical.

Now you need to put in curly arrows and you will have a mechanism for the isomerisation reaction.

[Rutherford]

I am not skilled at drawing mechanism, but I ended up with the one attached here. I didn't use enolates because I am not sure what H atom from what OH group would be replaced. I wrote previously that it is the H atom on the central OH group accidentally, but how to predict what H atom will be removed?

[Dan]

No, that mechanism is fundamentally incorrect. The arrow starts from electrons in a lone pair or bond.

See: http://en.wikipedia.org/wiki/Keto-enol_tautomerism

[Rutherford]

Huh, I got a hard time doing the one I attached now (I should've maybe lower the number of steps). Hope it's okay.