As far as "distictly Twins" aspects of TF (or maybe just unique aspects of TF in general), here's what I'm excited about:
The overall design of the exterior is very unique and very 'Minneapolis' so it will be easily and instantly identifiable with the Twins; also, the limestone exterior will be carried subtly throughout the interior of the ballpark (on the Admin Building, the overhang, behind homeplate, etc.) and will tie the exterior and the interior together nicely. Then you have the small footprint, which forced the Twins/HOK to get creative...I love it! Seems like they turned back the clock to the days of squeezing a ballpark in wherever you could fit one. Combine all of that with the canopy and I don't think you'll have to wonder whose park you're seeing on TV!
Plus, there will be an old school animatronic neon sign of the old Twins logo (twins shaking hands over the Mississippi) somewhere beyond the outfield stands, and the batter's eye will have evergreen trees planted in it (very MN). I also can't wait for Mauer/Morneau/Kubel to launch homeruns onto the plaza behind right field!
I'm sure I'm missing some stuff, Lafferty? Moose? Bombay?