The question is not whether you can be "denied" an appeal, but whether you can win an appeal. You have to show that it would have made a difference in your case if your attorney had made objections. If there were no grounds for objecting, then there would have been no reason for your attorney to object. If, on the other hand, there were grounds to object, you might be able to get a reversal if you can show first that a reasonably competent would have objected and second that you might have obtained a better result if the attorney had objected.
You raise a variety of issues on multiple fronts.
"WalMart" and "McDonald's" are proper nouns (not pronouns) and they are not copyrighted; they are trademarked. For example, you cannot open a restaurant and call it McDonald's and paint golden arches on the side of the building.
If you write an essay or personal narrative and talk about a time that you went to McDonald's, you can just write that. Generally, you can do the same in a work of fiction. (Example: Where the Heart Is by Billie Letts. The author used WalMart as the setting for a good bit of the story. She painted WalMart in a favorable light. I'm certain WalMart was made aware of this and given the opportunity to approve the story.)
In the movie "Little Miss Sunshine," there is a scene where the family is using some promotional glasses from a fast-food restaurant. Originally, the script called for drinking glasses from Burger King, and Burger King did not wish to be associated with the movie, so that detail was changed. That's about trademark.
If you write a report or an academic work, you must use the trademark sign immediately after names like WalMart and McDonald's and Apple.
Citing an author or an artist or a philosopher and referencing a work is not copyright violation. Citing a bit of a song's lyrics is one thing; printing the lyrics to an entire album is another. There are lots of factors.
You should read about what copyright is to get a better understanding.
Also, if you were to publish, the publisher will vet the work to make sure there are no legal issues. If you want to self-publish, you would do well to have an attorney (one who specializes in publishing) vet the work for you.
Generally, in order to be held liable, there must be stakes, preferably high ones. In other words, no one is going to bother coming after you unless it's worthwhile. This is not to say that this gives you a license to violate any copyright as you please, but rather to understand that it's a long way off before it becomes a problem.
I don't think there is a link listing any and all "legal issues concerning publication." There is much to be considered; it's not all just black and white.
In the meantime, don't worry about it. Write and get the writing done. You can fuss with the details and the legalities later.