Problem #1: Authors complain that the definition of "planet" doesn't include exoplanets (because they don't orbit the Sun)..
Solution: Change definition to include other stars or say that the particular star doesn't matter if the other criteria are met.
Problem #2: Authors complain that the criterion that a planet must "clear its orbit" is imprecise and is dependent on other objects.
Solution: None needed. Let the IAU define the border cases. As for being dependent on other objects, the point is that for an object to be a planet, it must utterly dominate its orbit, leaving nothing significant.
Problem #3: By the IAU definition, Earth was not a planet for the first 500 MYears of its existence, because it hadn't yet cleared its orbit. Authors call this "bizarre and absurd".
Solution: Why is this a problem? There was no guarantee that the Earth was going to survive as a planet. Another Theia-like impact could have ended it.
Problem #4: It is a linguistic paradox (and vindictive to boot) to say "a dwarf planet is not a planet."
Solution: So what? A guinea pig is not a pig. Spotted dick is not a dick. Etc.
It never ceases to amaze me how emotional the "Pluto is a planet" people are and how the MSM gives these people much more publicity then they deserve. In the immortal words of Neil DeGrasse tyson, "Get over it!"