I would wait to see how Nikon will (and if) continue to position the D610. IMO the specs for the D610 vs D750 are so close, if I needed to buy a new FX body in that range, I'd wait a bit and get the D750. But on the other hand the D610 is a great body and I agree with Gorf, I think you're going to see the D610 drop in price. The Nikon USA site has D610's on sale for $1,799 which seems to me is about $100 less than just a few weeks ago.
I don't think oil is going to be an issue. I can't believe Nikon would go through all the trouble of introducing a new model to fix their previous mistake, and then repeat that same mistake? Highly unlikely. Especially since oil spots are not common in any of the other models (at least that I am aware of). That says Nikon knows how to build a shutter correctly so they must have done that for the D610.