Your question is very general.
You want a stability issue, just try reading a 700 MB file or call a DLL with a wrong type.
Like any other compiler, LV has bugs which can cause stability issues, but those bugs mostly appear either in badly written code or in less common situtation. For the most part, LV is stable and a properly written application should run with no problems. LV also saves you many of problems involved in properly defining things and does all the memory management on its own, which can save you some headaches.
As far as security goes, most people implement some kind of security within their code to protect the application from being illegaly used. You can also choose to remove the code from built applications.
I suggest you post some more details about what it is you want to do with LV and what you're worried about.
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