I've got a few 45 including Kimber, Colt and Springfield. I recommend you look at them side-by-side. Do the slide wiggle test, very slight (almost non-existent) side-to-side movement. Tighter is better.
The barrel wiggle test is very slight (again almost nonexistent) barrel movement when you stick your finger in the muzzle and wiggle from side-to-side and up/down. Again tighter is better.
The barrel fit check is press down from above with the thumb on the portion of the barrel visible through the ejection port. There should be no movement if the barrel feet are properly fit to the slide stop.
Examine the barrel shroud (the squarish projection on the top/aft portion of the barrel seen in the ejection port). It should be a close tolerance fit to the notch in the slide, but should not drag when the slide is retracted. The slide should retract smoothly and go back into solid lockup when released.
Check that the magazine will drop freely when the magazine release is depressed.
Check to make sure the thumb and grip safeties work. Pulling the trigger should not drop the hammer when safeties are engaged nor should the hammer fall once the safeties are disengaged.
Finally, check trigger pull. It should be crisp with little overtravel. The Kimber II has the funky firing pin block safety. I don't know if Springfield has gone the same route.
Good luck.