I was wondering about vintage tremolos. Not locking ones, just vintage, fender style ones.

They're all pretty much the same design, right? So if for example I replace the one on my cheap ibanez with one from a quality brand (eg. Schaller or Fender), would that improve tuning stability in any way?

I think it's all down to the number of springs in the back cavity. My guitar only has 2. All cheap guitars I've seen have 3, Fenders have 4 or more.

Does the tremolo unit ITSELF (not including springs) make much of a difference?

It's just that, I've seen guitars with non-locking trems that stay in tune very well when you dive n' stuff (Van Halen's and Randy Rhoads' guitars, PRS, Fender) etc.

A good setup is essentian for tuning stability. I did a setup myself for my ibanez, and now it's only the b string that goes sharp when i dive. The others stay in tune enough for rock n roll
I have no idea what I'm talking about. Don't belive me.