I have both issues with my car. The stumble is not serious, so I don't bother, but I notice too that it usually happens when the compressor clutch engages. I figure its just the motor momentarily slowing down under the increased load.
The front vibration, as has been mentioned, can be caused any number of worn parts.
I had vibration during braking, so naturally, I replaced the front rotors. I still had the problem after this. I eventually replaced the rear rotors and the vibration under breaking stopped. Even though the vibration seemed to be coming from the front, it turned out to be warped rear rotors.
While I had the wheels off, I cleaned the rear hub of a buildup of rust and corrosion debris. This can be a hidden source of uneven rotor wear and shimmy.
In short. Make sure your rotors are clean and in good shape, and make sure your hubs are in good condition and rust/debris free.