As promised, I have replaced the throttle actuator TPS during the weekend.
Although it immediately solved the hesitation problem, I would not yet declare it as "the fix".
I am cautious because by replacing the TPS I have also performed a throttle reset. During the work, the car has been sitting for 5 hours without power (negative battery lead disconnected). Other users' experience shared here in this forum has shown that what was initially thought to be a solution was proved bogus by a revived hesitation within 500 Km.
After replacing the TPS I drove only 225 Km (~140 miles). Considering that I use the Z4M only during the weekends, you may want to wait another week for my next report. I planned a 400 Km (~250 miles) trips for the next weekend (Aug. 4/5).
On the other hand I am quite optimistic, considering that I have performed numerous throttle resets in the past, and none of them had such an immediate positive impact on the hesitation issue, as it happened after replacing the TPS last weekend.
But only mileage will tell
Here's some info about replacing the throttle actuator TPS. The itself job it's simple, but if you've never removed before the intake manifold then it's great to have the BMW TIS software at hand. Time needed: cca. 3 hours.
1. You need to buy a throttle position switch (TPS) p/n 13637840383.
2. Remove the top section of the air filter housing. Picture:
http://82.78.8.129/mye28/z4/TPS/TPS_pic1.jpg.
3. Remove the intake manifold (also known as airbox or air collector). Picture:
http://82.78.8.129/mye28/z4/TPS/TPS_pic2.jpg. Note that you can remove and then refit the airbox to throttle bodies clips without the special tool. For reference, check this thread:
http://www.z4-forum.com/forum/viewtopic.php?f=9&t=40502.
4. In order to take out the TPS, you must remove the two Philips screws. Picture:
http://82.78.8.129/mye28/z4/TPS/TPS_pic4.jpg.
5. Here's a view of the throttle body with the TPS removed. Mind that you must take out the green O-ring of the old TPS, as the new TPS comes with its own. Picture:
http://82.78.8.129/mye28/z4/TPS/TPS_pic5.jpg.
6. Refit everything back.
Suggestion: while you're there it's a good moment to clean the idle control valve (ICV) and the throttle bodies. You must remove the ICV, clean it and then fit it back. It's very easy. For the throttle bodies, push the actuator level by one hand to open the throttle butterflies, and carefully clean each throttle body and butterfly with the other hand. You need a carburetor cleaner spray and some clean rags. Make sure you don't drop anything down the intake!