I had the same problem with my Z. Picked it up from the dealer (20 miles on the clock) and the paintwork was rough as feck to the touch.
Later on during the "detail" I found out what was actually wrong - this is a piccy of the drivers side glass AFTER I'd cleaned the glass with glass cleaner!
Turned out the whole car was covered in what appeared to be overspray! Haven't a clue where it came from but needless to say I was very p*ssed off!
Anyway, here's what I did, hopefully it'll be of use to you:
1) Rinsed the whole car off with clean water from a hose.
2) Snow foamed the car and let it sit for 10 mins (you could miss this stage, but seeing as I was going to be doing loads of cleaning I thought I might as well do every stage)
3) Rinsed the snow foam off, then used Megs Hyperwash and lambswool mit and two buckets (one with water & megs in it and one clean water to rinse the mit). Then rinsed the car again.
I made sure that during 1-3 above I paid particular attention to wheel arches paintwork edges, under the sills and under the front and rear bumpers - it's easy to forget and skip these bits, but they usually harbour the most of the dirt and grit.
Usually at the next stage I'd waffle towel dry the car, but seeing as I was going to be claying anyway there's wasn't much point.
4) Next up was the clay. I didn't want to use anything too abbrasive on a new car, so used Sonus Ultrafine Detailing Clay, along with with Sonus Glyde Detailing Clay Lube. As it was quite a sunny day (not ideal) I didn't want to spray down too much of an area at a time, so did a two foot square area at a time and sprayed the clay bar too, then rubbed the clay bar over the panel and sprayed the panel as I went along, panel by panel. You can hear the roughness actually disappear as you go - just move along once the scratchy noise goes and use plenty of lube. Probably took an hour or so to do the whole car and another 30 minutes to clay the bl**dy windows!
5) By this stage the paintwork was lovely and smooth but not amazingly glossy yet. First up was a coat of Sonus SFX-3 Final Finish polish, applied by hand using a foam disc pad, left to haze, then polished off with a microfibre cloth.
6) Next was a coat of Sonus SFX-4 Paint Sealant, same application, left to sit for 10 minutes to cure and stick to the car, then polished off with a microfibre cloth again.
7) Last up was a coat (If I hadn't been so knackered by this stage I would have done two coats), of DoDo Juice Blue Velvet hard wax, applied with a foam disc, left to haze then polished off with a MF cloth.
Job done! Paintwork it amazingly glossy and smooth as glass!!