Not sure if this is the case for the 325, but my '02 M3 was acting weird
like that and there was a known cold start problem that they supposedly
fixed at the dealership. It ran great on the way home from the dealership,
but the very next time I drove it, it was acting the same way, only mine
generally 'skips' all the time. It's really running like sh.t, so back to
the dealership we go! Maybe if you called the dealer, they may know
something about a cold start problem for the 325 as well.

HTH.

Deb Moore
Phoenix Yellow '02 M3 CiC

Drive it directly from the cold start to the dealer.  Have the
dealer check for a fault code indicating a misfire.  It will also
indicate the misfiring cylinder.  Track down the problem from
there.

In my case, a problem very like the one you described was caused
by a mouse nesting near one of the coil packs.  A quick blast of
compressed air solved it permanently!

JRE

Same issue with 99 328i  
changed gas
changed spark plugs
checked gaskets
reprogrammed computer
added fuel line cleaner/ injector cleaner
Multiple emails to BMW Canada .... followed by car in shop for 21 days...
Still no solution.

But after an extensive search I found a person with the same problem that
had the poblem fixed.  The dealer changed the "idle control valve".  My
BMW dealership refused to change it because the "computer" said it was
fine. But it was so dirty it did not operate properly.  The policy not to
guess what is the problem is only what the computer told them what was
wrong made me live with it for over 2 years.  I ordered the part online
from some BMW oem place($120). I planned to put it in myself but...could not
find where. I brought it to the dealership and paid them $114 to put it
in. When they put it in they said the hose that feeds it was broken and
also needed replacing...(sounded like a scam to me but told them to go
ahead) WOW it runs smooth now.  Who would have guessed...an "IDLE CONTROL
VALVE" could control the idle.... not the dealership.  So for the risk of
a couple of hundred bucks I fixed the problem.  Previously my idle would
fluctuate as high as 1500 and down to 500... now steady at 700 except when
a.c. comes on and dips 100 or so.  Good luck