This is the classic Colt "out of time" condition.
If you slowly cock the hammer and the hammer cocks before the cylinder locks, the gun is out of time and should be repaired.
AS LONG as the gun does lock before the hammer drops in double action or you cock the hammer just a little faster to make sure the cylinder is locked it's usually safe to shoot.
However, if you pull the trigger in double action and the cylinder isn't locked and you're getting off-center primer hits, STOP SHOOTING IT.
The gun is firing in an unlocked condition and the bullets will soon be hitting the forcing cone in the barrel enough off-center that the gun will be spitting bullet metal back in your face.
If the gun isn't locked when the hammer drops the gun is UNSAFE to shoot.
The actual problem is usually that the hand that advances the cylinder is worn. In the older Colt action this repair is considered to be a normal maintenance item on a worn gun.
Depending on the gun this can be as simple a repair as stretching the hand. If the hand is too worn, or has already been stretched once, the hand may need to be replaced.
Since new hands are pretty much not available any more, this can be a problem.
What I'd suggest is to send the gun in to the Colt factory or to Master pistolsmith Frank Glenn.
Either will be able to diagnose the problem and correct it.
DO NOT take your Python to a local gunsmith.
Very few locals these days actually understand the Python action and don't have any of the specialized tools needed to repair them.
What you all too often get back from locals is a gun with the original problem not corrected, and other problems caused by misguided attempts to fix it.
This usually results in even more expensive repairs at Colt or Glenn.
I suggest you don't accept a locals word that he's a Colt expert or take local reputation as in indication that he actually understands the Colt's.
Pythons are simply too expensive to take risks with.
Colt will be at least somewhat slower because of their work load. Glenn seems to be a little faster. Your choice, both do top of the line work:
Colt's Manufacturing Company LLC > Customer Services > Repair & Refinish > Firearm Repair
Frank Glenn-Glenn Custom Complete Gunsmithing Service Glendale AZ
You can personally send your Colt in to either by shipping it via UPS or Fed-Ex. You CANNOT SHIP VIA USPS. Only a Federal licensed Dealer can ship pistol through the US Post Office.
The repair facility can ship the gun directly back to you.
The price of shipping through UPS or Fed-Ex is expensive because they demand the gun be shipped by the fastest possible method.
This is to have the gun in their system as short as possible to prevent their own people from stealing it.
When you ship you'll have to tell them it's a pistol. DO NOT LIE. Some fools tell the shipper it's "machine parts" or something other then a gun.
If the gun is lost, stolen, or damaged during shipping the shipper will pay you NOTHING, because you lied and broke the legal contract.
Be prepared for a counter person to tell you that you can't ship a gun. Simply ask to speak to a supervisor who will know what their own companies rules are. If he doesn't know ask to speak to a higher person until you find one who does know.
You cannot ship a gun at a UPS Store. These are not owned by UPS. You need to take it to a UPS depot.