Does Occam's razor have any limitations?
That is to say, are there any philosophers/philosophies which find little use for this scientific and philosophical rule? If so, who/what schools of thought?
Though you need not be concerned with the following aspect in your response, I am particularly interested when Occam's razor is applied within the field of computer science and engineering where "...the simplest of competing theories are to be preferred..." does not always produce the best results.
I am particularly interested when Occam's razor is applied within the field of computer science and engineering [...]
An software engineer's perspective:
Occam's razor is bit more subtle than 'simplest is always the most correct'.
First: 'simplest' is very subjective. Facing a server crash, I could theorize: a bad piece of code, solar flare, a dead squirrel in the rack, the CPU falling of, or just an act of God. At some level, the first reason is the least simple. However Occam's razor doesn't call for 'simplest', but for the fewest entities. From that perspective, it recommends looking at an explanation involving just the code and the hardware it runs on before introducing a squirrel (or God) in the system.
That said, Occam's razor also says that entities shouldn't be multiplied without necessity. And if after looking at the code and the hardware configuration, I can't find a good explanation for the crash, introducing the squirrel might become necessary (yes, it did happen).
Similarly, it might be necessary to introduce relativity to Newton's gravity when it proves insufficient.
There are some pitfalls: it's easy to get enamored with the most mathematically elegant explanation, or dismiss inconvenient new data that goes against an established (or favorite) theory. But those are issues unrelated to Occam's - a scientist unwilling to consider relativity or a conspiracy theorist unwilling to not consider aliens are equally guilty.
As long as Occam's razor isn't used to justify intellectual dishonesty, it's a pretty useful guiding principle.
No, even writers who reject specific theories despite Occam's Razor still use Occam's razor all the time. That's because Occam's razor is just a principle of common sense without which no coherent argument can be made. It's a necessary part of communication and rational thought.
Without Occam's razor, an argument would always have to made by explicitly discarding infinitely many theories. Instead, when making any argument, any writer implicitly assumes his argument does not need to mention the infinitely many other more complex ways any sentence could be understood.
Though if you look for an easy example of a philosopher rejecting the result of Occam's razor, then Pascal's wager would seem to be quite obvious (though Pascal makes only this one exception, and does not generally reject the usefulness of Occam's razor).
Ocean's razor has the severe, but by design limitation of being a simple heuristic, a rule of thumb that, when understood, can help you prioritize your investigations.
I, too, found it pretty dumb for a long time because I was introduced to it by the movie Contact, where it's used like a proof, dismissing the alien hypothesis without inquiry, which it is not meant to do. As this movie is probably the most prominent introduction of the Razor in pop culture, I suspect Jodie Foster is sadly the reason why so many people got the wrong idea about it (but I still love you, Jodie).
It kind of disagree with your assessment about engineering. Surely, the simplest system might not always be the right solution, but the simplest system that does the job is certainly preferable to an unmaintainable, impossible to concisely document mess of a solution (notwithstanding economic constraints like reuse of legacy systems, production costs and technological debt). I have done a lot of debugging in my youth, and Occam's razor clearly helped me prioritizing my investigation by looking for silly mistakes before looking into a possible but improbable compiler bug.
