My mom's been doing crossword puzzles for many years now, and as such occasionally enlists the help of my dad or myself when we might know more about something than she does. Being naturally interested in puzzles myself, I often sit by while she does them, and to her lament I often complain about various things, which is the subject of this post.
First Complaint
Crosswords are stuck in the past. Occasionally you see a clue that references something more modern, but it's usually something from The Simpsons, or music, or anything else from popular culture that's blandly mainstream. Dr. Dre shows up fairly often, actually, usually clued as "Rapping doctor" or something similar.
You occasionally see individual clues that lead to putting in video gaming-related things like Mario or Sega, but they're never prominent, they never appear more than once per puzzle, and most certainly never appear as the theme when a puzzle has a theme.
The most obvious examples of crosswords being stuck in the past are clues that ask you about movies from the 1950s or musical artists whose entire fanbase is either dead or in assisted living these days.
Second Complaint
Crossword-ese. These are words that, when you look up the clue on Google, all of the results are crossword websites. You never see these words outside of crosswords, and you just have to know them. Personally, I feel as though I've failed at solving the puzzle if I have to break out the almighty Google to get an answer. Crosswords should be solvable just by looking at the clues and using any letters from crossing answers that you might already have. Crossword-ese, on the other hand, leads to there being entire chunks of puzzles that you just can't get any letters in, which makes the puzzle less accessible.
Third Complaint
Circularly-referential clues. You'll see this as something along the lines of these (hypothetical) clues: 10 Across: See 15 Down. 15 Down: With 10 Across, something obscure. This does nothing to make the puzzle accessible to newcomers or seasoned solvers, as the only way to get either of those answers is to get enough of the answers to the clues that cross them that you can fill in the blanks. There is the random possibility that the clue that actually hints at one of the two parts will actually pertain to something you're familiar with, but for that to work, you just have to know it, which kills a puzzle's accessibility.
Fourth Complaint
Factual inaccuracies. These should technically be picked up by whoever edits the puzzle before it goes to print, but sometimes, issues like these escape even the best of the best. To be fair, it happens, and we're all human beings who make errors and miss things. It's just really annoying to have to deal with when you're working on the puzzle. My mom was doing a puzzle recently that had a clue along the lines of "Chinese dynasty following the Han". Well, I looked it up, and the next period of China's history is the Three Kingdoms era, with the kingdoms of Wei, Shu, and Wu, none of which were dynasties. Yet, the answer was "Wei". Ideally, this clue could have been rewritten (edited, if you will), to be similar to "One of the Chinese Three Kingdoms", phrased as such to steer people to the Three Kingdoms era of China where the answer is relevant and actually correct.
Fifth Complaint
Misspelling things just so a clue will work with a given answer. Seasoned crossword veterans call the shorter answers that comprise the majority of a puzzle the "fill", and this is an indication of bad "fill" that should have been reworked. Honestly, Crossword-ese is also an indication of this.
Sixth Complaint
Trivia clues. These are things that you just wouldn't know unless you happen to be intimately familiar with whatever they're talking about. All too often there's something like "City in the zip code 12345", where the only ways to get the answer are to get answers that cross it, or look it up. Again, having to look something up means you've already lost, and makes the puzzle less accessible.
Seventh Complaint
Clues whose answers are multiple words, and that give no hint of this. I'm not talking about the tacked on "(2 wds.)" cheat thing that some puzzles have. If an answer is more than one word, it should either be obvious from the subject that the clue relates to, or it should be subtly hinted at in the clue. This usually falls back into the category of "you just have to know", which, as previously stressed, makes the puzzle less accessible.
Eighth Complaint
SAT words. These are similar to crossword-ese, however, they're actually found outside of crosswords in very rare circumstances, such as in old people's speech and on the verbal section of the SATs. They're typically long or obscure words that have much more concise and modern synonyms, yet people stick to using the less modern and concise versions so they can feel smug when younger people have no clue what they're talking about. These reduce a puzzle's accessibility, because when you encounter one, you have to fill it in from crossing answers, and then when the puzzle's done you just sit there scratching your head and saying "that's a word?".
Overall
I'd love to get into doing crossword puzzles, because I love solving puzzles. However, somebody, somewhere needs to start making puzzles that are accessible to people under the age of 50. More video game and 1980s/1990s references would be a start. Themes based around those would be better. Involving internet culture would just bring the cancer that is internet culture to the print media and alienate the 99% who have no clue how to use a computer other than to look at websites and check their email. I've advocated for accessibility all throughout these complaints, so we don't want to reduce it even further in the process of catering to younger generations.
And just to address this before it comes up, the word "meme" is not just a fancy synonym of the word "joke", nor does it accurately refer to pictures with caption text in the font "Impact" edited in. Those pictures are more accurately referred to as "image macros". No one single person decides what is and isn't a "meme", memes happen organically as the result of things happening. True "memes" are more similar to the pile of in-jokes you and your friends and family probably have.