I copied this off the internet a couple of years ago. Don't know who wrote it, but it's very accurate as to what you need to do.
My '71 250C shifts perfectly from 1st to 2nd to 3rd to 4th. Just as described below.
Based on my experiences, FIRST make sure you have NO vacuum leaks. Make sure the metal tube vacuum line coming off of the rear of your intake manifold is connected securely at the manifold and to the vacuum modulator. SECOND ensure that your carb linkages are adjusted correctly. THIRD keep adjusting the linkage that connects your carb linkage to the transmission until you get the shifts where you want them. With that linkage disconnected or missing your car will most likely start off in second and shift into third and fourth quite rapidly.
I hope this helps you. I struggled with mine off and on for months before getting it to where I was happy with it. Good luck to you.
The later automatic used in your car is the K4C 025 and was used in this model from May 1969 through June of 1972.
It is easily identified by it's four bolt transmission pan as you observed.
Shift points on this version are regulated by rpms, accelerator position and engine vacuum.
There is a metal vacuum line which runs from the intake manifold to the vacuum modulator on the right side lower part of the transmission.
In addition a linkage rod runs from the engine to the transmission.
This linkage rod originates under the intake manifold and is attached to the accelerator linkage lever.
It runs back to the transmission where influences modulator pressure and shift points depending on accelerator position. During engine repairs this linkage or the engine accelerator linkage can be mis adjusted causing shift problems in the transmission.
It is critical to have the engine linkages set properly before performing linkage adjustments on the transmission.
There is a procedure for setting the engine accelerator linkages.
Stu Ritter wrote an excellent article in the Nov.-Dec. 2003 issue of " The Star Magazine" on the mechanical injection systems. He covered engine linkage adjustment and setting along with much more. Very worthwhile reading.
I also have the factory set up procedure for the linkages.
So if you do not have any references here I can post this information also.
Anyway, after all the engine accelerator linkages are set to specs, the transmission should shift as follows:
With the shift lever in " D" with low accelerator pedal input the transmission should shift from 1st to 2nd at around 5-6 mph, then shift from 2nd to third at around 17 to 18 mph, then shift from 3rd to 4th at around 24 mph.
At full accelerator pedal but (not kickdown), with the transmission in "D", the shift from 1st to 2nd should occur at around 22mph, the shift from 2nd to 3rd should be around 32mph, and the 3rd to 4th shift should occur around 56mph.
Depending on the rear axle ratio these figures may vary slightly.
Changing the shift points can be done after setting the engine linkages to specs.
Simply shorten the the mechanical linkage going from the engine (below the intake manifold) to the transmission simply by screwing the threaded ball joint inward or outward.
Lengthening the rod will lower all rpm shift points.
Shortening the rod will increase rpms of all shift points.
Again I stress set the engine linkages first since this will often cure shift problems and make the engine run better!
Some other possible problems not due to linkage adjustments, may be a bad modulator valve.
These screw off the side of the transmission and can be replaced.
There is also an internal adjustment here but a bit complex since the transmission modulator pressure should be monitored with a gauge during adjustments.
A bad modulator may have a ruptured diaphragm and trans fluid will show up in the intake manifold and on #6
In this case a new factory set modulator valve is installed.
Internal problems are always a possibility but not likely if your shifts are all too high or all too low.
This information is not relavant to early automatics used in these cars (K4A 025) with the 16 bolt transmission oil pans.
These tranmissions have different mechanical inputs for the shift points.