Keyboard Lag: This also is really terrible. I bought Swiftkey awhile back and have used it on many phones, and typing on the GS4 is incredibly laggy. I type very fast but not always accurately. The GS4 skips letters all the time. I know the phone is recognizing I hit the keys cause I use the key sounds and I can hear it click when I hit letters, but the phone will randomly skip letters. This happens in email and SMS. (I use Handcent for SMS). I don't type long things in other apps to know if it lags in there also, but I would bet it does. I know it's not swiftkey, cause I also have that issue with the regular keyboard, and Swiftkey was fine on the Note 2 and my LG Optimus G Pro.
I also have an LG Optimus G Pro for my work phone, and in many ways it is far superior to the GS4. The GS4 is nothing but a newer GS3 with a bunch of gimmicky stuff that most people turn off and won't use. The LG Pro is a great phone and runs very smooth, but I couldn't see buying it for my personal phone being as I doubt it will ever get much support since it is only on AT&T. Also LG is known for slow to non existent updates, so who knows if this thing will get 4.2.2, let alone 4.3 or above.