The rate of change is a potential problem. How many million years did it take after the dinosaurs for 8C of cooling? The ocean rising at a rate that puts LA back underwater in 100,000 years wouldn't cause much trouble, but what if every coastal city needs to fight off the sea Dutch-style within just 100 years? Hundreds of millions of people could be displaced, with widespread social, economic, and political effects.

Instead of robots that can use stairs, I just deploy robo-servants on each floor. I also have a specialized robot, named "Otis", for moving things between floors.

citation needed

When looking at changes in the ranges that various plants and animals inhabit, that could be evidence for or against.
When looking at changes in glaciers or sea ice, that could be evidence for or against.
When measuring temperatures of the atmosphere and oceans, that could be evidence for or against.
The majority of the evidence says that global warming is happening, and that human activities do play a role. "Global warming is happening" and "human activities contribute to warming" are pretty much settled science. This doesn't mean "accepted as unquestionable truth" but that profound contradictory evidence would need to be found.

How much warming will happen, how quickly, and what the consequences will be are matters of less certainty. Unfortunately the lesser certainty occurs precisely where answers are needed in order to make socio-political decisions regarding what steps, if any, should be taken to limit global warming and mitigate its effects. People who insist that warming cannot possibly be happening or that human activity cannot possibly be a significant cause are equally unhelpful as those who insist that "the science is settled" and drastic measures must be taken immediately without regard to the non-climatic consequences.

The very Wikipedia article you linked to says to use PTE bottles, because some glass bottles will absorb the UV before it gets to the water, and that the leaching of material from plastic bottles into the water has been studied and found not to be of concern.