As to using DosBox with non-GOG games, I believe that there are a number of front-ends available that might make it easier to set up your games. You should find a list here.

On the other hand, the principle of Full Disclosure suggests that disclosing vulnerabilities (which Open Source may encourage) should reduce the window during which the vulnerability is open to exploitation. It also suggests that wider knowledge of vulnerabilities should encourage the development of solutions, both in terms of outright fixes and in terms of stop-gap programs. Meanwhile, exposure of the source, while making vulnerabilities more visible to malicious eyes, should also produce a wider pool of potential sources for fixes and stop-gaps.

[edit] Come to think of it, as long as you download it from the official site (or, I presume, in one of the games provided by GOG), DosBox being open source shouldn't incur any increased vulnerability to hackers: unless they manage to get to the code used by the core developers (which shouldn't be much more difficult than with a closed-source developer, I suspect), what you download should at the least have been vetted by the developers.

The only real potential that I see for hacking would involve either you downloading DosBox from some a dosgier source, or the hacker getting to your computer itself (in which latter case, why would they bother with DosBox, having already gained access to your computer?).

DosBox is safe, it just's emulates old DOS hardware to play games. The GoG installer even sets it up for you.
so it's perfectly safe.