When adding things outside of Linux to Linux, you are (vastly) increasing the chance of backdoors, viruses, and a myriad of related problems. Running Windows programs within Linux is a good way to get there!
Proprietary software, like Windows, is most-often closed source, meaning that people outside of Microsoft do not get to review the actual code for bugs, errors, omissions or backdoors.
A backdoor is a portion, or many portions!, of the code left open to hackers; either intentionally or by error. A backdoor can be used in many ways, by known or unknown people. It can be used to compromise your system, your contacts, other data and even your hardware (see Stuxnet).
This issue is not isolated to operating systems though. Using any closed-source software carries the same risks.
With open source software -- anyone can review the code for errors and security holes such as backdoors. You have multiple sets of eyes looking for problems and this has been a tremendously successful way of improving software.
By default -- some Linux distributions default to including only free software. #Debian is an example of this.