A mixed construction is a sentence with incompatible elements that begins with one type of structure and shifts to another type of structure. In these sentences, the speaker sets out to say one thing and abruptly switches to something else resulting in confusion.
As a refresher, think of the sentence as a mathematical equation with the following structures:
Subject + predicate = sentence or Phrase + clause = logical connection
These will always make sense as distinct equations. However, one component of an equation is mixed with a component of another equation, the meaning becomes unclear. For example, consider the following revision:
Beginning in the fall of 1997, we began to charge students a trash tax, was the responsibility of student government. (Mixed Construction)
Beginning in the fall of 1997, we began to charge students a trash tax. The student government was responsible for this project. (Revision)