Some MSDOS viruses were (and are) capable of infecting various EXE's and other files throughout the filesystem through modifications. If you mount your whole drive, you are opening your system up to infection by old MSDOS viruses. It is likely that some of these viruses would render a new Windows executable useless, since the authors made assumptions (re: executable structure, the platform, etc.) that were true at the time of writing, but which are no longer correct. For this reason, even a relatively innocuous virus from the past could be quite destructive (although incapable of using the new host executable for further reproduction).
There is some good news... To my knowledge, many old viruses were quite primitive and were incapable of seeking out new executables for infection. Sometimes, another executable would not be infected unless you manually ran it after the virus has become resident in memory. Since you probably won't attempt to run a Windows executable from under Dosbox, any files you have mounted that are unrelated to Dosbox should be fairly safe from these ones. Were there other viruses more intelligent than this though? Likely, yes. Were they widespread enough that we should take precautions against them? Maybe.. I'm no expert. Some people would prefer not to take this chance since it is an unnecessary risk.
Someone else mentioned that old apps made assumptions about Windows that are no longer true. This is another example of an old and broken assumption leading to destruction. It's better not to put your applications in an environment where their assumptions are incorrect, and in which they have been untested. Predicting what may happen when the application goes into an untested environment isn't an easy task, in part because it is generally no one's priority to analyze each app in detail to see everything that it does and report it to everyone. The detailed workings of the apps you're running are unknown. So if you put it in with your new files, you might be unlucky enough to get the first taste of its negative side effects in a new environment.. as unlikely as it may be.
Personally, I put all my Dosbox games and applications under single root directory which basically acts as a virtual harddrive. It's no trouble for me, since I prefer this kind of organization anyway. Of course.. my Dosbox executables aren't safe from the effects of other Dosbox apps, but that's an acceptable risk to me because nothing I run under Dosbox is critical.