"...But very importantly, I suggest to all my readers who have not done so yet, make scientific skepticism a part of their work..." - can you define in more detail, what did you mean by scientific skepticism?
I like the idea, but I see a possibility of a somehow diametric interpretation here. Did you mean scientists being 'scientifically' skeptic towards unfounded ideas or people (even scientists) being skeptic towards their own 'scientific' discoveries and beliefs.

"A scientist can’t prove. Only disprove. And whoever disproves a more established theory gets the most prestige." I like this one, with the prestige part being somehow irrelevant to me.

Did you mean 'scientific skepticism' as being maximally critical towards your own scientific beliefs and findings? Cause this is what I believe has lately been missing in our scientific circles. I think we all know where time, costs and profit are directing research towards; and secondly fully independent research in capitalism being a myth.

A lot of people blindly follow some arguments labeled as science, mentioning some supposable research studies 'that have shown...' . I also believe that a lot of scientific facts today are based on somehow false or incomplete statements. If not, then we are just too full of ourselves, absolutely sure that all our discoveries are indisputable, bullet-proof.
But it seems only normal - even in science - that we are in a certain stage of evolution and some today's known facts can be refuted, disproved in future, even those that seem 100% correct today. I tried to describe this in one of my latest posts with generational differences in families. To me this could be understood as scientific skepticism - scientist's rule no.1: 'Always doubt all your findings'.

I believe that we are skeptic towards some new inventions, discoveries, but we almost never show any skepticism towards the scientific foundations - facts that even these new discoveries rely/are based on. For example, our medical science was certain for a number of years that high body temperature needs to be regulated and carefully maintained below certain levels. Lately they are slowly realizing that it's one of immune system's own mechanism and needs to be left alone to do its job. If you're interested in the topic, you can read more about it here, or even better - do your own research!

Nevertheless, I am a huge proponent of development, new technologies and evolution. But I fear that much too often we see discoveries and new technologies being pushed hastefully to broader use or production. All in the name of short-sighted instant profit, only to hear later 'we could not anticipate that' or 'practice will show'. Our current generations are losing sense for waiting, discipline, necessary due time for things to come, appear, finish. We want everything immediately, instantly, no waiting or delay is tolerated.