This definitely sounds like the start-up clutch as I had the same problem with my last SE CVT-7 on a ’06 plate at 33,167 miles. It is a known fault on the Jazz due to a design fault in the mechanism and/or CVT-fluid – Honda have modified both.
Fault manifests itself as a faint judder / vibration when starting off lasting only a few seconds at about 15-25mph. This took a bit of messing about with the dealer to get the problem sorted.
First, they did a CVT gearbox flush and fluid change [4 Nov 2011], I then had to take the car away and return it after 200 miles [23 Nov 201] for them to re-check whether the fault had cleared; they confirmed that the slight vibration was still present.
I then had to return the car for a third visit [30 Nov 2011] for the dealer to replace the start-up clutch which they did within a day (impressed with this as it is quite a big job – strip down/re-build)
ALL THIS WAS DONE FREE OF CHARGE & TREATED AS A WARRANTY CLAIM..........at that time!
Apparently, this fault with the jazz cvt gearbox has a warranty extension applied to it by Honda giving 7yrs or 100k whichever comes first, this is covered in a Technical Service Bulletin [Number: HUK000000001117] which clarifies the situation, ALL CVT-7 jazz`s with chassis build code GD1 from 02,03,04,05,06 are included in this extended warranty, it covers as a first measure flushing the gearbox & if that doesn’t work then replacement of the clutch with the modified version.
Footnote: I also had problems with the Exhaust Gas Recirculation (EGR) valves on a ’52 plate Sport CVT-7 and the later 06 car but this manifests itself differently with a “chugging” noise on cold start ups (particularly prominent in winter after standing overnight on the older car). On the newer ’06 car the engine developed an erratic jerkiness; this is distinctly different to the start –up clutch fault which is consistent each time you move off from standstill. Both replaced FOC under warranty.
Bottom Line: Get it into the dealer for appraisal but expect a few visits to get the clutch replaced FOC!