Perhaps a word first on "exploits" vs "software vulnerabilities". A software vulnerability is when your bank prompts you for a password and you discover you can crash the website by pasting in the text of War and Peace in place of your password. The crash has revealed a software vulnerability which could, perhaps, reveal a weakness in the software that lets you gain control over the server it's running on. This requires some specialized knowledge, namely how the code works on a machine level. If you had no idea what hardware the machine used, or how that hardware functioned, then taking control of the machine would, well, be exponentially more difficult, at least.
An exploit, however, is just a flaw in the design of the program that lets you do something you're probably not supposed to be able to do, and requires no knowledge of how the hardware works. This comes up all the time in video games. You discover that if you, say, drop some money inside your house in the very moment you are stepping outside, the money ends up inside your house and also still in your pocket. Classic duping exploit!
With this in mind, my thoughts are:
Classic hacking, controlling the servers, rewriting the software: very unlikely. Even if you found a bug that gave you a way to inject code into the computer running the simulation, your complete lack of knowledge of how that code works would give you no real starting point on trying to change it. (I'm thinking it's really unlikely that the computer running the simulator we might be living in would be anything like the computers we are familiar with inside the simulation. The outside computer might not even have the same laws of physics we experience.)
Exploits that let you do things you aren't supposed to do: more plausible. You never touch the actual simulator code, you're just exploiting loopholes. Arguably, all of science has been trying to find loopholes. Maybe electromagnetism is humanity exploiting a loophole in the coding of our simulation. Turns out you just run electricity through a wire wrapped around a nail and poof, it's a magnet! Hacks!
Perhaps someone has discovered something, though, something fairly simple, that allows a broad base of "exploits" to be used, from walking through walls to "duping" real world items. Now that the secret is out, the Reality Guard has to try and destroy this knowledge, as well as anyone who figures out how to use it. (One thought on this: it's "debug mode" aka "god mode". Meant to be used by the developers of the simulation to come in and test things without being hampered by the reality of the simulation. Sims are not supposed to be able to enable it...)
On the other hand, though, you can pretty well do what you want here. Wreck-It Ralph featured an arcade character that figured out how to hack arcade game code from inside the game, probably because it was conveniently arranged in a way he could literally see, understand and manipulate, in an entirely unrealistic fashion, but hey, it was a great movie.