I think the list posted by the OP is one of the worst I have seen lately. Normally I expect a list like this to have some questionable inclusions, but that is normally attributable to differences in taste. Including ST:IV and Timecop, and to varying degrees Hercules, the One, and Time Traveler's Wife, make me shake my head.
ST:IV: As other posters have said, just because you can come up with alternative solutions for the problem of the whale probe doesn’t mean the movie is bad. The solution was logical and the movie was fun, what else do you want.
Timecop: not the best time travel story, but good action, a charismatic lead, some campy dialog and a sense of fun. Again, a decent movie.
Hercules: Just because the gods are still wearing togas and it’s 1980s in New York doesn’t make it a time travel movie.
The One: alternative dimensions, not time travel.
Time Traveler’s Wife: the article writer and some others (sorry, Kibbin) seem to be focused on the title but forgetting that it is the time traveler’s WIFE. The movie and the book it is based on are really a romance story where instead of work or friends or money being a barrier between the couple, time travel is (it’s a stand-in for emotional separation). Not the greatest movie, but adaptations of larger works often fall short because they were not originally written to fit 125 pages and 90-120 minutes.
Putting these movies on the list of worst time travel movies ever makes me question the article writer’s ability to understand words like “worst”, “time travel”, and to read more than the blurb on the back of the dvd case.
Relatedly, I just watched “Timecop 2: The Berlin Decision”. Also not one of the worst time travel movies ever. A lot of the beats in the movie (differences in the “present” that the hero cop is surprised by when he returns from a mission, and the return of previously dead characters to the hall’s of the timecop facility) are pulled straight from the first movie. While the production budget is much lower, the story is a little obvious, and the time travel logic a little less sound (though the launch chair is better in this one), the movie still works well as a true sequel to Timecop.
I also watched “Time Bandits” recently after hearing so much good stuff about it, and I was bored enough that I didn’t even finish watching the movie.