Swift Feather-legged Fly.
Common Whitetail female.
Red-spotted Admiral.
Nessus Moth.
Or rather, flying things, since it’s hard to get a good picture of insects in flight. We can try, though. Dusky-winged Hover Fly.
Spot-winged Glider — the spot on the hindwing is sometimes even subtler.
Cuckoo leafcutter bee.
Meanwhile, an Asian Tiger Mosquito attempts to draw blood through leather boot, and sock, and skin. Nice try, lady.
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This work by Matthew Wills is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Backyard and Beyond 
I think your red-spotted admiral is a red-spotted purple.
Yes, you’re right. Some confusing taxonomy here. Red-spotted Purple is a subspecies, Limenitis arthemis ssp. astyanax. There’s also an SW/Mexico subspecies: azinonensis. The White Admiral subspecies, found further north, is Limenitis arthemis arthemis. There’s a hybridizing border between the two.
Great shots!