Background: The development of scientific software applications is far from trivial, due to the constant increase in the necessary complexity of these applications, their increasing size, and their need for intensive maintenance and reuse. Aim: To this end, developers of scientific software (who usually lack a formal computer science background) need to use appropriate software engineering (SE) practices. This paper describes the results of a systematic mapping study on the use of SE for scientific application development and their impact on software quality. Method: To achieve this goal we have performed a systematic mapping study on 359 papers. We first describe a catalogue of SE practices used in scientific software development. Then, we discuss the quality attributes of interest that drive the application of these practices, as well as tentative side-effects of applying the practices on qualities. Results: The main findings indicate that scientific software developers are focusing on practices that improve implementation productivity, such as code reuse, use of third-party libraries, and the application of "good" programming techniques. In addition, apart from the finding that performance is a key-driver for many of these applications, scientific software developers also find maintainability and productivity to be important. Conclusions: The results of the study are compared to existing literature, are interpreted under a software engineering prism, and various implications for researchers and practitioners are provided. One of the key findings of the study, which is considered as important for driving future research endeavors is the lack of evidence on the trade-offs that need to be made when applying a software practice, i.e., negative (indirect) effects on other quality attributes.