For cylinder end shake the Colt factory spec is for no more then 0.003".
Anything over that requires repair.
To measure, push the cylinder to the rear and hold it there as you gage the barrel-cylinder gap with an auto feeler gage.
Then push the cylinder forward and hold it as you gage again.
The difference is how much end shake you have.
Continuing to shoot a Colt after it's past 0.003" will batter the gun to death.
Unlike the S&W and Ruger's you cannot repair end shake in a Colt with washers. The repair involves using a special hydraulic tool that squeezes the collar on the front of the cylinder with a hardened steel support stud inside the cylinder hole.
Few to no gunsmiths ever had that device, and unfortunately Colt has shut down most older revolver repairs.
I can recommend Frank Glenn in Arizona. He's a Master Colt qualified pistolsmith who does work to factory standards.
His price and turn around is excellent and members on the Colt Forum who use him give him top recommendations.
http://glenncustom.com/
As for rotational movement of the cylinder revolvers like the S&W, Ruger, Dan Wesson and newer models of Colt's like the Mark III and later work very differently then the older models of the Colt's.
In the older Colt's like the Detective Special, Python etc when the trigger is pulled the cylinder is forced into a tight non-movable lockup and held there.
Within reason the harder the trigger is pulled the tighter it's locked. (Don't over do it, you can damage the action).
The old Colt actions are checked for tight lock up by pulling and holding the trigger back while checking the cylinder for any rotational movement.
There should be none.
Other guns like the S&W, Ruger, etc and the later Colt's like the Mark III the cylinder is deliberately allowed to be loose with the trigger pulled.
This is to allow the bullet passing from the chamber to the barrel to force the chamber into alignment with the barrel.
For that reason the cylinder is specifically designed to allow the needed looseness.
Even in a gun that seems to lock tightly, there's still enough backlash built into the action to allow the needed movement.
In these guns holding the trigger back is not a valid test for anything.
How much looseness is allowed in the cylinder with the action cocked or uncocked is not a factory spec for Colt or S&W.
The test is; Is the revolver accurate, and does it spit bullet metal.
If it's accurate and not spitting, it's good.
So, in your case is end shake over 0.003", is it inaccurate, and is it spitting bullet metal?
If any of these are the case, you need to talk to Frank Glenn.