It's not necessarily that you don't see the differences, it's that your brain doesn't consciously process those differences and take note of them -- but it may well do so subconsciously. Designers look for these things automatically, so in their case those things will be processed consciously (and they won't be able to improve on them before they've consciously processed the differences anyway, so this is important to them).

But does registering the details unconsciously matter? Possibly. Not quite about blurrier buttons but I've read a study recently on the effects of good typography vs bad. In the study, participants couldn't tell apart good typography from bad, but experiments showed that better typography positively affected their mood and even productivity (I wrote about it here: You don't necessarily need to have the differences pointed out to you in order to feel them and be affected by them. The Google experiment demonstrates this as well.

It's up to you whether you have the resources to optimize every detail. Unpolished designs have never stopped good products from succeeding, but it doesn't mean that good products should remain unpolished, or that there is nothing to gain by doing it. We should strive to do the best work we can, within the limits of opportunities we are given, which means that if you don't have the resources then it probably isn't wise to spend all the time polishing an early product, but if you have higher ambitions and want to build something to last, then the details will matter as they will be noticed over continued use.