'Contradictions' in Star Trek?

It has recently come to my attention that a certain group of uninformed amateur film critics have been spreading misinformation about Star Trek containing numerous "plot holes and contradictions", which they deem "nits". This article is intended to demonstrate that such accusations are groundless and only intended to preach to the choir of the lowest common denominator skeptics, the ones who seek out plot holes in the most trivial details and argue that this somehow proves Star Trek is mere fiction.

The article I'm critiquing can be found somewhere or other. No, I'm not telling you where it is unless the author embarrasses me in public. Quoted sections are in yellow tables, with applicable responses below them.

Link