1998 Z3.. Manual Trans shudder under acceleration in 2nd gear as it nears 2000 rpms, then goes away as it approaches 2500 rpm's.. Any suggestions?.. Thanks

When you say "sputters at 2000 rpm" , are you referring to ANY time the engine is at 2000 rpm - meaning in Park, when you are just goosing the throttle, or in gear when you are accelerating, or at highway speed in high gear? If you are experiencing a "shuddering" in the engine at certain speeds/rpms - especially if these are speeds you regularly cruise at (long commutes at steady speeds), the problem could be in the Throttle Position Sensor (TPS). They have a tendency to wear unevenly if you drive a certain steady speeds. Eventually, the problem would progress to an engine code, but it may occur without setting the check engine light.

clogged catalytic converter

MAP sensor may be going bad letting it over fuel the engine causing black smoke and bogging RPMs .

There are a few conditions that will not set a code. For example, stumbles are often caused by ignition coil problems. If the problem persists at a certain RPM, could be an O2 sensor problem in closed loop operation not lasting long enough to set a code, or a fuel regulator or injector problem. I would get a good code reader and check readings from all sensors in the circuit (including misfires) to see if you can pin down the problem.

look at your coolant. if it looks like coffee or its thick or beige in color, than you need a transmission and radiator replaced. your radiator failed. the build in cooler to be specific, which caused your trans fluid to mix with cooant and trans got contaminated,. your trans is junk.need to replace it with new radiator. make sure to flush out your trans cooler lines also. some of the contaminated fluid gets trapped inside of them. you want to have the system clean as much as possible.

With normal acceleration the 1st to second shift point should be around 2500-3000 rpm. Most of your shifts under moderate acceleration will take place at this same point or when there a light load on the transmission. Under hard acceleration the RPMs will climp higher due to increased power needs and the computer will shift when less power is needed or the RPMs climb to an unsafe speed say5000-6000rpms (depending on where yours redlines). Also going up a steep hill will raise the RPMs higher and goind down a hill will cause a faster shift at lower RPMs. These can always be altered by an individual owner by adjusting shift points, using performance parts and if you have problems (low tranny fluid/trans issues). Your trans RPMS are fine and will vary depening on how your foot accelerates. The shift pattern should be the same every time you drive slow/medium/fast/, look for changes in those patterns you will also catch a problem early.

My monte carlo would hit 2nd gear and bog down and not shift properly until it got to the last gear. I had the catalytic converter replaced and that fixed that problem. (It also created another, but not near as bad)

SHift solenoid pressure switch

Being it is a manual transmission and the engine was removed, it is likely the clutch and pressure plate not releasing completely at high rpms.

Sounds like the timing belt tensioner. I have that problem. Rattles at low rpm, goes away as you acceralerate. Looking to have timing belts changed and tensioners replaced.