There are two possible problems: the coder could be lazy and leave bugs in the code OR the company could put mischefful code in the program (perhaps to make more money from the user).
Open source might fix problem #1, as some people will poke around to see if they can write a paper about the bugs. Open source is really good for #2, that sort of thing makes the person that finds it famous.
Closed source does make #1 a little worse because few people check the code. Closed source always makes #2 possible because the few checkers have the same boss as the person adding the mischef.
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