Specifically, the gradient crawl that evolution gives must yield viable organisms among every step. If something is within a local maxima that cannot be climbed out of while remaining viable, then evolution can't do anything by definition. That doesn't mean that a better global maxima doesn't exist, and an organism engineered to a better state.

On the other hand, organisms are generally very "fault tolerant" systems in the small—if you get a crucial gene copied, and then one of the copies mutates to do something weird while the other remains functioning, the resulting organism is probably going to be viable, since the weird thing that the mutated copy of the gene does will [unless it's some very specific type of "weird thing" it's producing] be treated by the body as just another foreign enzyme to xenometabolize or foreign antibody to attack.

And the organism's genetic line can persist with that mutant gene indefinitely, building onto it until it becomes a useful feature.

(This isn't so true in especially small organisms, where an extra gene here and there might blow their size or resource budget. This is one of several things constraining the evolution of mitochondria, for example.)

In such incredibly high-dimensional landscapes, such a thing as "local maxima" basically does not exist (you need a local minimum in every single dimension at once). Not to mention that in this case it's not a continuous fitness landscape - you can make wild jumps in each evolutionary step, so the situation of "maximum that can't be climbed out of under given constraints" is even harder to come by.