This is one of the best vanos solenoids out on the market right now.
jumping like does it feel like it is coming from the transmission or the engine; The vibration?
1) Sounds like maybe turbo charger surge; if you have a turbo charger?
2) perhaps you might have collected soot on the valves stems on the way through the intake. If it is turbocharged?
3) It could be that you might have a clutch throwout bearing going or the clutch entirely if you have stick shift?
4) It could be your fuel filter if you have a petrol engine version?
5) finally it could be your timing chain
I would still pull the valve cover and check the stability of your upper guide rail. With a small l.e.d. flashlight making sure it does not wiggle around. Just changing stuff like the Timing chain tensioner could help recover it some what.
The upper guide rail and become loose altogether and throw the plastic down into the engine. And a timing chain is not accompanied by a code.
It all comes down to two things whenever I have had a problem with my R56 that being.
1)Getting out to the garage and jacking it up.
2)Then putting it in the Radiator service support position.
Number 1) is harder to do than number 2) sometimes. For the fact that the car sits so low. and requires a jack with a small piece of a 2 by 4 about 14 inches long under the sub frame molded rail to get a jackstand on the rubber block.
Once I get it to that point. Then it becomes easy to see leaks, problems,etc.
It can be anything at that point. I would not focus on the clutch or throw out bearing. It sounds engine related. A upper guide rail for 50 dollars U.S. and a Chain tensioner for 50 U.S. could put back whatever that problem is until next year or so. If you accompany it with a round of new spark plugs and buy a coil so that the day it starts to miss you have a brand new one to swap out testing each coil and finding the mis fire that way. It probably would not hurt to do a oil change and air filter change also.
If you upper guide rail is questionable be careful replacing it. It's probably O.K. seeing how you more than likely have the N18 or N16 engine. Which never really had that problem. Still yet having a new plastic guide for the chain is not gonna hurt it nor is a new timing chain tensioner. I would also check for air leaks. If they replaced the Vanos then they more than likely removed the intake manifold. I would remove my intake manifold and use some
O-Ring Silicone Grease | Super Lube
and coat each gasket for the intake in that. I would look down in behind the intake where the turbo actuator vacuum line is and zip tie them with small zip ties.
[as seen here just barely little white zip ties] two black braided hoses right next to eachother on the vacuum reservoir.
Then re install in the intake manifold. Then I would get in the zone and start checking the entire air induction system to that intake manifold tightening up air intake plumbing. I have the turbo so I would check the actuator arm vacuum hose the other end of the picture of the hose I put here that the intake manifold covers up; then I would zip tie that end of the hose.
With or without a turbocharger I would still check for air leaks as the map sensor on the intake manifold requires the numbers(amounts of air) to match the M.A.F. sensor. Like a count room in a casino. If the numbers don't match we have a problem.
If the problem is deep in the engine it would be the timing. Timing does go out on the N16 and N18 engines.
To make a long story short you don't have any warning lights on.
1.little flashlight shining down into the timing chain housing for worn or broken parts.
2.checking the upper guide rail for stability.
3.little zip ties on the vacuum reservoir
4. superlube o-ring grease on the intake manifold gaskets and re install
5. checking for air leaks all across the induction pipe work.
6. zip tie on the vacuum hose on the turbocharger actuator.(on the turbo)
7.new round of spark plugs with 1 new coil swapping then driving to see if that makes a difference. Different brand of spark plugs(that might be what you need to do to begin before anything else. spark plugs advertised are not a electrical value fit for any all mini coopers.
8. New tensioner It can't hurt, not that pricey; just be careful removing your new vanos solenoid to get to that.
9.New upper guide rail. with the hope in mind it does not lead to replacing the lower guide rails now.
10. If the car is under warranty keep taking it back and request a new timing chain. [THAT FAMOUS ARGUMENT] they should do that for you.

1) Sounds like maybe turbo charger surge; if you have a turbo charger?
2) perhaps you might have collected soot on the valves stems on the way through the intake. If it is turbocharged?
3) It could be that you might have a clutch throwout bearing going or the clutch entirely if you have stick shift?
4) It could be your fuel filter if you have a petrol engine version?
5) finally it could be your timing chain
I would still pull the valve cover and check the stability of your upper guide rail. With a small l.e.d. flashlight making sure it does not wiggle around. Just changing stuff like the Timing chain tensioner could help recover it some what.
The upper guide rail and become loose altogether and throw the plastic down into the engine. And a timing chain is not accompanied by a code.
It all comes down to two things whenever I have had a problem with my R56 that being.
1)Getting out to the garage and jacking it up.
2)Then putting it in the Radiator service support position.
Number 1) is harder to do than number 2) sometimes. For the fact that the car sits so low. and requires a jack with a small piece of a 2 by 4 about 14 inches long under the sub frame molded rail to get a jackstand on the rubber block.
Once I get it to that point. Then it becomes easy to see leaks, problems,etc.
It can be anything at that point. I would not focus on the clutch or throw out bearing. It sounds engine related. A upper guide rail for 50 dollars U.S. and a Chain tensioner for 50 U.S. could put back whatever that problem is until next year or so. If you accompany it with a round of new spark plugs and buy a coil so that the day it starts to miss you have a brand new one to swap out testing each coil and finding the mis fire that way. It probably would not hurt to do a oil change and air filter change also.
If you upper guide rail is questionable be careful replacing it. It's probably O.K. seeing how you more than likely have the N18 or N16 engine. Which never really had that problem. Still yet having a new plastic guide for the chain is not gonna hurt it nor is a new timing chain tensioner. I would also check for air leaks. If they replaced the Vanos then they more than likely removed the intake manifold. I would remove my intake manifold and use some
O-Ring Silicone Grease | Super Lube
and coat each gasket for the intake in that. I would look down in behind the intake where the turbo actuator vacuum line is and zip tie them with small zip ties.

Then re install in the intake manifold. Then I would get in the zone and start checking the entire air induction system to that intake manifold tightening up air intake plumbing. I have the turbo so I would check the actuator arm vacuum hose the other end of the picture of the hose I put here that the intake manifold covers up; then I would zip tie that end of the hose.
With or without a turbocharger I would still check for air leaks as the map sensor on the intake manifold requires the numbers(amounts of air) to match the M.A.F. sensor. Like a count room in a casino. If the numbers don't match we have a problem.
If the problem is deep in the engine it would be the timing. Timing does go out on the N16 and N18 engines.
To make a long story short you don't have any warning lights on.
1.little flashlight shining down into the timing chain housing for worn or broken parts.
2.checking the upper guide rail for stability.
3.little zip ties on the vacuum reservoir
4. superlube o-ring grease on the intake manifold gaskets and re install
5. checking for air leaks all across the induction pipe work.
6. zip tie on the vacuum hose on the turbocharger actuator.(on the turbo)
7.new round of spark plugs with 1 new coil swapping then driving to see if that makes a difference. Different brand of spark plugs(that might be what you need to do to begin before anything else. spark plugs advertised are not a electrical value fit for any all mini coopers.
8. New tensioner It can't hurt, not that pricey; just be careful removing your new vanos solenoid to get to that.
9.New upper guide rail. with the hope in mind it does not lead to replacing the lower guide rails now.
10. If the car is under warranty keep taking it back and request a new timing chain. [THAT FAMOUS ARGUMENT] they should do that for you.