Engine hesitates

I occassionally have engine hestitation, especially when I slow down at a traffic and about to pedal down to move again the engine rpm drops & I have to off the engine and restart several times before the engine picks up on good rpm to move again. Tried cleaning the Airflow sensor but no success. The system diagnosis reads the following;
1. PO420; Catalyst System Efficiency Below Threshold (Blank 1)
2. P0657; Actuator Supply Voltage Circuit/Open
3. P2116; Throttle Actuator control motor Current Range/Performance

I have a 2003 Corolla, and I just recently had the converter replaced. My wife is the one who drives the car more than I do. She noticed that it hesitates as she accelerates, it stutters a little bit like it's not getting any power, and then after she lets up on the gas and does it again it will accelerate. Can someone explain to me what could be the problem? I hope it's not a diffective converter. Thanx

That's just it the check engine isn't on. Did it once yesterday.

Check engine came on. I took it in to toyota and they said the code for the converter came on. I got a second diagnosis and the mechanic told me it was the converter.

When I start the car in cold winter temperture, after 30 seconds or so, the engine will stumble from approx. 2200 rpm down to about 1800-1900 rpm when car is warming up in the driveway.
Then climb back up as if nothing was wrong.
Does not stumble at all once the engine is warm, or while driving.
Somebody mentioned a "coolant temp sensor" being the issue.
Any suggestions?