It will not hurt you in any way to apply to more than one department at a time. However, if you are accepted to more than one department, you will have to choose which one of those departments you want to be admitted into. You can only be admitted to one department. Students also submit a personal statement that is considered in the admissions process. Admission is competitive for every department in the College of Engineering.
Some departments are considerably more competitive.
Students with GPA's below 2.5 are much less likely to gain admission to an engineering department. Please see an advisor to discuss GPA competitiveness. The main reason is that the pre-requisite classes tend to be more similar to departmental courses, and thus can give a better indication of how the student may perform once admitted into a department. Sometimes another engineering department will offer them admission. Other UW majors, such as Mathematics, Physics, Building Construction, and Chemistry may also be possibilities.