Not at all. No previous Mathematica training is required or expected. Students learn to use the Mathematica code gradually as they progress through the courses. The overwhelming majority (85% as measured by survey) of new C&M students with no previous Mathematica experience report they are comfortable within two weeks.
When I originally signed up to take C&M BioCalc for my freshman calculus course, my older brother tried to talk me out of it. He told me that I wouldn't learn anything, and that I would have trouble later on in my engineering classes. Out of stubbornness, I stuck with it. This past year, my brother came to me to ask my help. One of his mechanical engineering classes was filled with Calculus III material and he was having trouble. After I helped him, he said to me, "I wish I had taken a C&M course. I probably still would have forgotten all of the formulas, but at least I would know how to go about getting the answer."
Techs support both the lab machines and the software used in this program.
In the event of a problem, send an e-mail to tech@cm.math.uiuc.edu.