[dfariswheel]

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.

 

[dfariswheel]

Thanks very much. I actually considered that this condition must indicate a worn hand but the gun shows no signs of wear. I suppose it could have been man-handled at some point. I'll plan to send it in to Colt or Frank. Any idea about what a hand replacement/repair costs?

You'd have to talk to Colt or Glenn about cost, but they can't tell until they actually see the gun and determine what's wrong.
As above, the fix may be a hand stretch, or a new hand.
I hadn't thought about the gun having "Cylinder throw-by" where the cylinder is rotating too far and going past the locking notch.
In that case, repair may be a matter of bending a part.

In any case, no one can tell you an estimated cost until they see the gun.

As for having a problem caused by a worn hand, the gun wouldn't necessarily show any signs of abuse or even much use at all.
The hand is a normal wear part of the Python action and is considered to be a routine maintenance item on a gun with action wear.

In any case, STOP USING IT, until you get it professionally checked.

Just as a reference, here's my instructions on how to check the old style Colt action for correct timing:
To check Colt timing:

BOLT RETRACTION AND "SNAP BACK".
Open the cylinder and look at the small "lug" in the bottom of thecylinder window. This is the cylinder locking bolt.
Cock the hammer, and watch as the bolt retracts into the frame and pops backout.
The bolt MUST begin to retract THE INSTANT the hammer begins to move.
There MUST be NO (ZERO) hammer movement possible before the bolt starts toretract.
The bolt should retract smoothly with no hesitation until it's fully retracted,then it must pop back out with a clean "snap".
There should be no hesitation, and no amount of "creeping" back out.

CYLINDER UNLOCKING.
Close the cylinder.
Use your left thumb or fore finger to again cock the hammer, closely watchingthe cylinder bolt as you SLOWLY cock the hammer.
As the hammer comes back, the bolt will retract away from the cylinder.
The bolt must retract far enough to unlock the cylinder BEFORE the cylinderbegins to rotate.
If the bolt is still slightly engaged with the cylinder lock notch, thecylinder will be attempting to turn while still partially locked.
This produces a "catch" or "hard spot" in the trigger pulland will damage both the bolt and the cylinder lock notches.
This often appears as metal "pulled out" of the lock notches, withrounded off and burred notches.

BOLT DROP TIMING.
Continue to cock the hammer, LIGHTLY laying your right index finger on thecylinder just enough to prevent "free wheeling".
Watch for the bolt to drop back onto the cylinder. WHERE the bolt drops isCRITICAL.
The bolt MUST drop onto the leade or ramp in front of the actual cylindernotch.
If the bolt drops too soon, (in front of the notch ramp), it will mar thefinish of the cylinder.
The bolt should drop into “about” the middle of the ramp.
If the bolt drops late, (farther toward the actual locking notch) the revolvermay display "cylinder throw-by".
In this condition, during double action shooting the cylinder may rotate PASTthe locking notch, and fire in an unlocked condition.
It's the nature of the Colt action, that a hesitant or jerky trigger pull bythe user can induce throw-by in even a properly tuned Colt.
The Colt trigger should be pulled with a smooth, even pull, with no suddenjerks at the beginning.

CYLINDER LOCKUP.
Continue to pull the hammer back and both watch and listen for the bolt to dropinto the cylinder lock notch.
The bolt must drop into the actual lock notch before or just as the hammerreaches full cock.
The most common Colt mis-time situation is the hammercocks before the bolt drops into the lock notch. (Hammer is cocked, butcylinder isn't locked).
In this condition, with the hammer fully cocked, you can push the cylinderslightly, and you will hear the "CLICK" as the bolt drops into lock.
In my experience, most Colt's leave the factory with the bolt dropping a littlelate into the leade, but usually wear in to correct timing.
If the bolt drops onto the cylinder early, no real problem, but there will beextra finish wear.
If the bolt drops late (closer to the lock notch) the cylinder may "throwby" or rotate TOO far in double action and this can cause off-centerprimer hits and firing while unlocked.

Each of these checks should be done on EACH chamber. All of these checks arebetter done individually. In other words, do the bolt retraction check on allsix chambers, then do the bolt drop test, and so on.

A properly tuned Colt will:
Have a smoothly functioning bolt with no sticky or hesitant movement.

Unlock before the cylinder begins to turn.

The bolt will drop onto the middle of the ramp.

The bolt will drop into the lock notch just before or as the hammer reachesfull cock.

Have a smooth trigger pull, which does "stack" or get heavier as thetrigger is pulled.

 

[dfariswheel]

Colt factory specs for the Python trigger pull are:

Double action:
Maximum: 12 Pounds.
No minimum, but minimum is related to single action pull.

Single action:
Maximum: 4.5 pounds.
Minimum: 2.5 Pounds.

Sounds like your Python is well within specs. Attempting to lighten the single action pull can often cause trouble with mis-fires unless the tuning is done by a pro. Bending the spring just to lighten the SA pull is not the way to go.
Personally, I'd leave well enough alone unless you want to spend the money for a professional action job.

These days we now understand that smooth is better then light. Years ago people thought the lighter the better.