GIGO is an overused idea that's mostly meaningless in the real world. The only way for the statement to be true in general sense, is if your input is uniformly random. Anything else carries some information. In practice, for Babbage's quip to hold, the interlocutor doesn't need to merely supply any wrong figures, they need to supply ones specifically engineered to be uncorrelated with the right figures.

Again, in general sense. Software engineers are too used to computers being fragile wrt. inputs. Miss a semicolon, program won't compile (or worse, if it's JavaScript). But this level of strictness wrt. inputs is a choice in program design.

Error correction was just one example anyway. Programmers may be afraid of garbage in their code, but for everyone else, a lot of software is meant to sift through garbage, identifying and amplifying desired signals in noisy inputs. In other words, they're producing right figures in the output out of wrong ones in the input.