The only current work-around for the wake delay is to use a Smart Cover/ Smart Case (magnetic wake)
Waking from Sleep/Wake button or Home button both cause the delay
Waking from Smart Cover/Smart Case (magnetically) or by plugging into a charger does NOT cause the delay.
The current work around for the screen rotation issue is to disable Reduce Motion as below
If the Reduce Motion setting is turned ON under Settings/General/Accessibility/Reduce Motion, the screen will not rotate correctly
If the Reduce Motion setting is turned OFF under Settings/General/Accessibility/Reduce Motion, the screen will rotate correctly
An alternate & temporary way to correct the rotation issue
With the device on/awake, simply tap the Sleep/Wake button once to sleep the device, then quickly again to wake the device. This should cure the rotational issue until it reappears after the device has slept for longer than ~15 seconds.
Seems we are stuck with these issues & their work-arounds until Apple get it's act together and fixes them. Supply your feedback to them here please:
http://www.apple.com/feedback/