It sounds like you have a lean mixture. You might try replacing your intake gaskets and checking to make sure the surfaces are smooth and clean. Also there are a number of vacuum hoses and fittings on this engine that could be leaky when cold or a crack in your intake manifold that seals up when it warms up. Don't forget about the quick connect vaccuum fitting immediately behind the throttle body. You may be able to find the source of problems by spraying WD 40 or some other flammable spray onto areas of the intake manifold and hose connections while it's cold until you hear a difference in engine smoothness.

After checking on three possible sources for this information including one in Germany. Nobody seems to have the info.

I finally found the problem. It seems that the mechanic who changed the engine broke the original crank sensor connector and replaced the pins. But he got them wrong!!!. This was discovered by viewing a number of You Tube videos and I happened to see the correct color code for a brief second on one of them. I was able to get a new connector and contact pins from the dealer as separate parts. Total cost of about $30. I had to crimp extension wires into the new contact pins myself. This can really only be done correctly with a special contouring wire crimper made for that type of connecting pin. I have that tool in my work tool kit because I do machine wiring. Then I connected the new wires to the old ones with a splicing connector because the originals were cut a bit short so they wouldn't reach the connector without a fight. I checked the signal output of the crank sensor on the bench with an oscilloscope wired both ways. The wrong way didn't produce any signal while the correct wiring showed a clear signal. So why did the car run at all? I thought the engine wouldn't run without a crank sensor signal???? If it will run in limp mode without a crank sensor signal why doesn't the dealer know this??? FYI, I did ask the dealer about the correct color code way early in this process and they were not forthcoming with the info. I could have fixed this three weeks ago with that info!! They suggested that we bring the car in for another analysis and diagnosis for an estimated $1000.!!! Aren't BMW's Great!!

I agree with Rich Sheffey to check for difference in bulbs. Even with the same part number, mistakes in manufacturing happen. Another possibility is that the reflector mirror coating inside the tailight lamps is different between sides. If both were purchased from BMW they should be the same but if they are not the same, the dimmer one should be replaceable under the parts warranty. Your picture seems to show that the tailights on right has a red section in the center and the Left tailights are amber and white. Is that an illusion?

I also heard from the dealer that electronically the two designs are the same so I filed down the centered tab on the coilpack as far as I could but that didn't allow the connector to seat. So I filed a new slot into the coil connector shell to match the new coilpack using a jewelers needle file. Now it fits and works OK. Just wish I didn't have to booger up the parts to make them fit.

I didn't see any video in BMW workshop that pertains to what I did. The videos show that the computers have to be recoded if you add something to the engine that wasn't there originally and that makes sense. Nothing functional or electrical was changed in my case. Just the mechanical complete rotating engine. In fact, the original crank sensor from the original engine was installed into the replacement engine. Not sure which video do you think pertains?

No. Didn't think it necessary or possible. According to BMW dealer all N52's are the same. But recoding seems to make sense after all we've checked. Exactly what would recoding do? especially if all N52's are the same. The only thing I can think of is that the crank sensor gear has a different pattern that may be "serialized" to the engine and that would be very crafty of BMW but possible.