cold start vibrations

[chinym]

dear all, after introducing myself in the newbies section, it's time for my first post here. i've recently got myself a e46 328i, year 2000. The power of this car is excellent and the condition is great. previous owner serviced it exclusively at auto bavaria and i have the service records. problem with the car now is that during cold start, the engine would vibrate non uniformly, as if it is misfiring, for about 1 minute or so. after that it would idle fine, with uniform vibrations. condition seems to be worsened when the engine load is increased, ie, when the aircon is turned on. i've recently checked for vacum leaks and doesn't seems to have any. changed the air filter as it was quite dirty and condition seems to improve marginally. otherwise i'm thinking of fuel pressure, and ignitions. what should i check next? and how would i go about it? thanks in many ways.