Appearance just means, as you say, appearance of the phrase. Television programs are specified because they are saying the phrase can’t be used at all by a television program (except in terms of parody/satire, which are exempt from the TM provisions, I believe), but it could be used by, say, a magazine review of some computer components. Of course, IANAL, so I might be mistaken.
Walt should have called me! I’d have licensed the use of my (identical but unreated) surname to him cheap! 
I don’t think that this is trying to indicate “appearances in the field of motion picture critiques.” It’s “television programs and appearances” when those programs or apperances (on television) are “in the field of motion picture critiques.”
The reason that a newspaper review would be implicated is not because the newspaper review is literally within this category, but because its use is close enough to the type of use that Ebert makes that it is likely to cause confusion amongst consumers. People are going to think either (1) that the newspaper either has some kind of affiliation with Ebert or is using the phrase with Ebert’s permission or (2) that the phrase is not really something that Ebert has an exclusive claim to. Ebert is allowed to act to dispel both these misconceptions.
That wouldn’t have worked. He’s not barred from using his family name because it is his family name, but because its use would cause confusion with the Coca-Cola wines.
Thanks for the explanation. I didn’t see the connection between Taylor Wines and Coca-Cola at all.
Didn’t R.E.Olds of Oldsmobile fame suffer a similar fate, i.e. he lost the rights to his own name - which is why his later creation was named the R.E.O. Speedwagon?
It’s not just that they object because of possible loss of rightys to the mark – Polar Beverage had a much better right to the polar Bear image, having used it much longer. Coca Cola , however, had the weight and economic power to batter Polar into submission. The touchiness of megacorporations with regard to trying to get exclusive rights to words and symbols goes beyond mere protection into absurd bids for exclusivity – as when Ralph Lauren sued the publishers of “Polo” magazine (which is, after all, devoted to the sport, as was using the name long before Lauren was).
I understand all of this except for how the phrase “two thumbs up” was able to be approved for trademark. “Thumbs up” is a phrase in common usage, and I would think “two thumbs up” would be no different.
It’s like trademarking “Hello” or something like that.
Now if they had trademarked “Ebert and Roper’s Two Thumbs Up” that would be different.
Common phrases can’t be copyrighted, but they are available for trademark purposes when applied to very specific situations. That’s how Trump was able to trademark “You’re fired.”
Anything - including a color or a sound - can be trademarked if associated with a particular product.
They were able to show it is different. Likely, they were able to show that “two thumbs up,” in particular, was not commonly used for movie reviews. That two makes all the difference. Plus, by the time they registered the trademark, they were probably able to show secondary meaning, meaning that by using it, the phrase had become associated with them and no one else.
Colours are very tricky. It’s rare that you can get exclusive rights to a colour alone. You have to have massive proof of secondary meaning. Also, the colour can’t be something naturally associated with the goods. And the trademarking of colours can’t lead to some producer down the line being unable to find any colours to use.
He should have called it Big T’s “I’m Not Touching You” W(h)ine. 
Sometimes, however, the little guy wins a minor victory: Burger King of Florida, Inc. v. Hoots, (1968), in which the Burger King of Mattoon, Illinois and vicinity is allowed to keep using that name as long as it does not expand beyond Mattoon, Illinois and vicinity.
Just as an aside, this Burger King is absolutely nothing like the franchised Burger King, but it is good.
Goes to show how important and pervasive trademark is when I had a mental disconnect while eating there. “I’m eating at Burger King,” I thought to myself. “Does not look like Burger King, does not taste like Burger King, does not smell like Burger King.” And they even had a pinball machine.