They are reliable for things they are "designed" to. For example for motoric coordination, coordinationg body automatic functions - breathing, pumping blood, etc. They are also highly reliable for new things, if properly trained - like playing music, riding bike, flying plane, playing games, etc. Parsing natural language is not easy task, it involves symbolic processing, yet brains are better at this than computers.
Complaining that brains without training are not reliable is like complaining computers don't work correctly without software.
BTW - many of the errors brains make are not because of unreliable parts, but because of system design - we have some firmware that made sense before, and now is problematic. This firmware is reliable - it works as intended, only now the problems changed, and we can't change the firmware, and patching this in software causes some problems.
It's difficult to say how reliable our brains are at doing things like driving cars or riding bikes because we don't really have anything to compare them to. I expect that it won't take long before we can build automated cars that are far safer drivers than any human.
Parsing natural language is probably inherently non deterministic since no natural language grammers are context free. When we parse a sentance there is almost always at least some ambiguity in the sentence itself, plus we also have to process other things that the person has said; in many cases years in the past and what motivation they may have for saying a certain thing. It is very unlikely that 2 people will get exactly the same meaning out of some natural language sentence because it comes with all kinds of side effects for example something somebody says may also change your opinion of them and other things they have said.
I suspect that if we cannot get deterministic behavior out of future computers because of the amount of parallelization required to make efficient use of their CPUs we will end up with 2 streams of computing , one of which will stay relatively static and be interested in using computers for the types of problems we currently do and another which will be interested in applying it to new problems that do not require determinism.
The software for these computers will be radically different so most likely you will have 2 computers on your desk (or in your pocket , or in VMs), one with < 10 cores and one with > 1000 cores.
I don't know much about how the brain works but I guess this is a process that uses allot of heuristics and psuedo randomness that probably lends itself well to being parallelized which is why we set up our languages this way.