It's because FindRoot evaluates psiwmax[g0] first with symbolic g0 and analyzes the result. This causes the error message. Then FindRoot evaluates psiwmax[g0] with numeric values substituted for g0, and everything works fine after that.
The standard way to prevent the error message is to define numerical functions using NumericQ to prevent evaluation on nonnumeric arguments. Wolfram has a Knowledgebase article on this.
Example coding paradigm:
ClearAll[psiwmax];
psiwmax[g0_?NumericQ] := ....
