I've always known my records, I think its the best way to overall improve mixing, and construct sets, i always try to memorise the beats but also I pay a lot of attention to the bass lines aswell, but what i try to do now is switch styles,i.e from a progressive trance track to a trance antheum, thats when I think memorising and knowing your vinyls works, but I admit I cheat every now and then and play tracks with a cold ending so it makes mixing easier especially when theres a tune no matter how many times i memorise it, and no matter how much attention I pay to it, helps me mix that track, cos some tracks can be complete bastards somtimes to mix, so I always keep a couple of cold and unlively tracks about, thats where i think knowing your records helps out a lot.

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of course it's important to know your tracks! I try to know them as well as I can. I listen to them at home and ask myself what track will mix good with this one.... I even remember all the names of my tracks. it's easier than choosing "track 5 on the blue vinyl" (I would say that way is pretty confusing)

and when I listen to my tracks, I imagine them in a set... will the crowd move to this tune??
so my answer to "how important is knowing your tracks", my answer is "very important". but that's just me. there are DJs who just know the start, ending, beat, and if it's a hit or not, and that's enough.
every DJ makes his judjement............

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