  Elizalde, Vanzo, and Zerbini have shown that the effective action of two free
Euclidean scalar fields in flat space contains a `multiplicative anomaly' when
zeta-function regularization is used. This is related to the Wodzicki residue.
I show that there is no anomaly when using a wide range of other regularization
schemes and further that this anomaly can be removed by an unusual choice of
renormalisation scales. I define new types of anomalies and show that they have
similar properties. Thus multiplicative anomalies encode no novel physics. They
merely illustrate some dangerous aspects of zeta-function and Schwinger proper
time regularization schemes.
