I bought a 1997 A4 1.8 about three weeks ago.
Generally, I love it.
Still, I notice some hestitation when I step on the gas, as if the car stutters a tad. And it doesn't only happen when I first start driving the car in the morning. (I do not warm my car up. I drive it immediately, but slowly for the first mile or two)
Has anyone ever had this problem?

I have a 1998.5 A41.85M and I notice it hesitates for the first minute of driving. I've noticed this after about 1 year of driving it. Im going to ask my dealer about it and I'll post something if he gives me any insight.

Later: Im Audi (Im outtie)

Many have posted here the same hesitation you are experiencing. Consensus is... it's normal! No one seems to have an explanation.