Has anyone used 3rd party testers?
I have a site that occasionally breaks, but there is no way of knowing why. If I knew why, I'd easily fix it, but I do not have anyone testing it much, prior to the public seeing it, so I was wondering how much would it normally cost to pay a 'testing company' to test their website, mainly for functionality on all sorts of computers/browsers but also just wild clicking and use that I never predicted? I imagine the price may vary from a few thousand, to a billion gazillion dollars, so I was just wondering if there is a reasonable institution that anyone might recommend.
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or is it completely custom? if completely custom, how was it written and in what language(s)? (ie, pure HTML vs. PHP etc.)
the reason i ask is that these days most sites are written on some sort of platform or framework, whether it's wordpress or django or what-have-you, and there are testing tools available.. in fact unit testing systems exist for every language and all the big frameworks/platforms that vastly simplify and isolate the test process from core code.
hence the time/cost will depend on how your site is written. for sure this is not something that you can fully automate the setup and trust the results. there will be set up involved in targeting each element/function you want to test, but depending on how your site is set up this might not be that big a pain. or it might be a real big pain.
that's why i ask.. 
unit tests have been around for a while. see, http://en.wikipedia.org/wiki/Unit_testing for a detailed description. basically to answer your question, 'yes, sort of..'
the tests have to be programmed. for instance, say you have a 'submit' button that's supposed to pass some POST data. you write unit tests for each little bit of functionality that needs to be verified. so say you expect the string 'Hello World' in the POST data in the example. you would 'assert' that the POST data equals 'Hello World'. if it does the unit passes the test (returns 'true'). if not then FAIL.
obviously this example is simplistic. it makes it very handy if you have a complex chain of events where bugs can get lost, because you can run and re-run a set of tests and get a big red 'FAIL' in one part of the code, narrowing down debugging by a bazillion percent.
they do take time to write, but best practices says, 'yeah, and..?'