Golf 3 TDI: Jerky Engine & Lawn Mower Sound

Hello,
My TDI has a problem where it shudders when accelerating in 3rd, 4th, or 5th gear. It's a slight shudder, almost like a gust of wind is pushing against it. When I read the error codes, it shows a faulty MAF sensor or ECU, which is pretty standard.
Furthermore, when I rev the engine to 4000 RPM in neutral, it feels like it's only running on two cylinders. After giving it a little gas a few times, it then runs normally again.
The VW parts exchange specialists are, as always, at a loss.
What should I do?
Best regards,

Why are you revving your TDI engine so high while it's stationary? Don't you like your car???
Regarding your problems, try using the search function. There's a lot of information available there. If you still have questions later, we'll be happy to help you here.

... Oh, a 1Z that's shaking... (sarcasm on) We've never had this before (sarcasm off)...

The search function will overwhelm you.

@bertil

That's just an 'urban legend,' a 1Z that's shaking...

Okay, enough joking around. I also had that jerking issue (diagnosed as a faulty mass airflow sensor). About three-quarters of a year ago, at around 138,000 km, a new pump was installed, and the problem went away.
Now, at approximately 178,000 km, the problems are starting again! For example, I notice it when I accelerate in 5th gear at around 1500 RPM; the engine starts shaking again. I'm also starting to think that the old pump could have stayed in, and that it might be a software issue.
Well, I'm not really that concerned about it. First of all, the pump is still under warranty, and secondly, I'm going to sell the car soon anyway...
(My next car will almost certainly have an ALH engine.)

Are you buying another Passat?

Best regards, WarLord.

I'm looking at a 2001 Golf Variant 'Edition' with 90 horsepower... Hopefully, it will work out.