The cop who got knocked out is much taller than the man who knocked him out, yet the uniform fits the knocker-outer perfectly.
When Mannix presents his identification to Carol Lynley it looks like the photocopy of a driver's license: it says "California License" but does not have the words "Drivers" nor "Detective" so, it is unclear what kind of a license it is. However it appears to be printed on newspaper ink upon a white plain background, and even his photo is in black and white and appears posed smiling, leaning at an angle towards the camera, which an official government photograph would not have allowed. And with such a fake looking identification, there's no way that Carol Lynley's character would have allowed him to enter her home.
Among the record albums Mannix was looking at for his "background music" were Iron Butterfly "In A Gadda Di Vida", Andy Williams, David Rose and Blood Sweat and Tears and the music playing did not sound like any of them.