That was such a weak argument - they saw little marks on her nose where possible eyeglasses were possibly worn -- and to think it was such an important point (although incredibly weak and silly) that it swayed the non-sweating man and several comments that well now we have a doubt and we must be sure in a murfer trial. This is sort of appalling to me. They should have asked the judge if this lady witness was wearing eye glasses when she saw the murder occur.
The problem with the "nose marks" argument in this movie is that the guy who wrote it (Reginald Rose) lends the false impression that IF the witnesses' credibility was in question because of her eyesight, it wouldn't have been "tested."
To put it another way, in trials, witnesses just don't get up on the stand, say what they want to say, and then leave. They get cross-examined, to see how well their testimony holds up. If they were telling the truth or weren't mistaken, their testimony holds up. If they were lying or incorrect, they trip over themselves.
IF it was implausible that she couldn't have seen the murder, you can bet your bottom dollar that the defense would've tested her somehow in cross-examination. The lawyer may not have brought up the question of whether she was wearing glasses or not, but she might have been grilled repeatedly about how well she saw the murder, to the extent of giving herself away as being mistaken, confused or lying.
The fact that the jurors believed that the woman's testimony was accurate implies that this is what happened--she was tested under cross-examination, and her testimony held up. With no way to discredit her, the screenwriter basically has Juror 8 start grasping at straws to undermine her credibility (look at the marks on her nose! look at how she was dressed!). What else could you do in that instance?
It's like that infamous moment in the OJ Simpson trial with the glove. The jurors couldn't reject the glove as evidence, so OJ's lawyer grasped at straws claiming that it couldn't have been his glove because it couldn't fit. (Never mind all the other signs pointing that it was his personal pair of gloves.)
It wasn't going to get tested because it didn't come up during the trial for whatever reason. The problem that we see in this film is that jurors are trying the case in the jury room, and basing it on speculation, and noone really seemed up to the task of arguing the other side.
Fun Fact OJs lawyers realized that the gloves weren't going to fit due to being outside and weathered, and having to fit over rubber gloves. They were considering having OJ put them on in court if the prosecution didn't. If they had, the prosecution could've argued the reasons by they didn't fit, but it's a lot harder for them to try and argue against their own gotcha moment.