2005 BMW X5 3.0 transmission issues... Please help!!

[dkl]

The different diameter tires front to rear is most likely your culprit now that I see the tire sizes that you're running. However, I would suspect the different tire diameters to cause transfer case problem on an AWD system. But then again, the weakest link in the drive train will fail given enough stress placed on it.

If it was me, I would start by putting the same tire size on all 4 corners. Then troubleshoot from there.

I didn't have any issues before the oil/filter change - just after using an aftermarket one did I ran into shifting issue. Going back to the OE BMW filter solved my problem.

[JCL]

If it was me, I wouldn't start with the tires. They would potentially cause a problem with the transfer case, not the transmission. And the codes would be related to the transfer case.

Neither would I focus on the DME or TCM.

You can conclude from the results when you are manual shifting that the clutches/etc can manage a shift when the transmission doesn't have to decide when to shift.

I would be looking to the transmission valve body, transmission wiring harness, speed sensors, actuators, solenoids, and other monitoring/control systems internal to the transmission that manage shifting.

Recall that failsafe mode is just the transmission protecting itself because it doesn't know what to do, based on lack of inputs from sensors, or inputs out of the expected range, or whatever.

You need a test plan that guides you to the likely problem components from the codes you are getting.