None here.
Where do you have your a/c and blower settings? For the 300C, they should be set on the Auto and LO indicator for front seat passengers, HI for the entire car. Then individually select the front passenger seat TEMPs.
Another point, this automatic system reads both the interior and exterior temps. If the temp is low enough inside vs outside, there will be minimal indications of any blower speed until there is a need for it. Further, in colder outside conditions, the fan will not blow until the engine coolant has reached a set warmth temp; this is to avoid blowing cold air. The owner's manual is pretty good on this automatic climate control operation.
I just leave mine set on automatic, let it select whatever, heat or cool, to fit the need. This also keeps the a/c compressor seals in use. It also blends in cool air to the cabin even in winter or rainy moist conditions, keeping down interior moisure. Likewise, the constant low fan operation filters the air coming into the cabin. The same system in my earlier '99 LHS ('98 build) worked fine in this manner over its entire 7 year period of ownership with no problems.
If yours is not working in this manner after being so set, you should get it back to the dealer ASAP. If the coolant is low, so could be the oil in the system. Running the system under such conditions could really mess up the compressor.