The most obvious issue that comes with the series is that it mostly exists as a promotion for said mentioned trading card game. Before I go into more depth with this issue, I should provide some quick history. Before the card game took off, the Yu-gi-oh manga source material created by Kazuki Takahashi was more focused on the ancient spirit of the Millennium Puzzle punishing evil characters encountered by Yugi and his friends with Penalty Games that inflicted ironic and often lethal punishments on the mentioned evil-doers. There is even a late-1990s anime adaptation of said series that Toei created covering these early parts of the manga. The card game end of the series came about in some episode arcs where Yugi and his friends got into the card game craze and crossed paths with diehard collector and game champion Seto Kaiba. This part of the series grew so popular that Konami started up their own version of the trading card game that continues to be popular to this day and said popularity led Konami to persuade Kazuki Takahashi to change up his title's story direction to focus more on the trading card game.
The influence of Duel Monsters' product promotional influence is rather obvious with the good majority of its title focus. In the same vain as Dragon Ball Z does for shounen battle anime, many of Yu-gi-oh's trademark card game duels often drag out for several episodes at a time and characters often get in the annoying habit of shouting out their moves, what the effects of their cards are, bragging that their strategies are flawless, and our heroic characters lucksacking (for non-card game players, lucksacking means luckily drawing the right card needed by chance) far too often when it appears they are down for the count. The mentioned lucksacking often involves the enemy duelist having some overpowered card or strategy that makes whatever our heroic characters are doing having them struggle to stay in the game until the hero conveniently draws just the card(s) they need to turn the tide of the duel.
Even with the card game promotion it does, the Yu-gi-oh anime also obviously does not properly follow the rules of the game that you would follow in real life. I will avoid getting into a long-winded rant about what rules are bent by the anime since it is not relevant for the sake of this review. But obviously, the anime will bend things with the rules of the actual game for the sake of plot convenience and advancement. A number of the overpowered cards from the anime when released in a physical format often have their effects altered or nerfed for the sake of gameplay balance in the real-life trading card game. Also, the rules used for playing the game in the anime are often quite different from the actual game and makes the following the anime not the most reliable means of learning to play the card game, especially with the rampant lucksacking and many of the character decks not being tournament caliber. Western players of the card game will obviously notice this with the Duelist Kingdom arc with gimmicks like land stat boosts and no tributes needed to summon higher-level monsters, while anything from Battle City arc and later is played more closely to the current card game rules albeit with lesser Life Points and some additional rules not found in the real-life game. However for those unaware, Duelist Kingdom arc follows an older version of the card game in Japan that is based on gimmicks following similar rules that the arc plays by.
Now let us move on to plot and characters. The gist of the plot involves the adventures of Yugi and his friends as they learn more of the origins of the seven Millennium Items, powerful Egyptian artifacts that possess various magical effects, and the ancient spirit that possesses Yugi's Millennium Puzzle. While the anime offers exploration of these story elements at points throughout the series, they are mostly overshadowed at points by the show's large focus on the card game duels and mostly feels like a backdrop to have a reason for the card games to exist at all. The characters do not get much fleshing out either as they mostly follow standard anime archetypes and exist either as cheerleaders supporting Yugi or other characters during their duels or as opponents built up to be threats until they are inevitably defeated by any major character in the series. Pretty much, plot and characters in this series are nothing but a hollow shell for this series to have its trading card game matches.
Many Western audiences will also be familiar with the infamous heavy editing done to the series by 4Kids. Obviously, many of the changes done to the series were done to make Yu-gi-oh appropriate and accessible to younger American audiences with character name changes, objectionable content such as violence and nudity being edited or removed, additional spoken lines of dialogue added that are not found in the original Japanese version, and removing any trace of Japanese dialogue found onscreen. Yet at the same time, these changes can make the series even more of a chore to watch through as they can be insulting to the intelligence of viewers. Mentions of the Shadow Realm are, in many instances, used for the series to get around cases where characters are in life-threatening situations or just got killed. Removing all traces of Japanese onscreen dialogue makes things ridiculous during the card game duels since the original version of the series had all the card text for the cards on them, while the 4Kids version only has the card graphics, stats, and level of each card played thus leaving some to wonder how characters could even know the effects of their own cards. But perhaps the most annoying addition to the series was its incessant habit of talking about friendship constantly throughout the series (the Japanese version also did this to a degree, but not as rampant) and made the character of Yugi's gal pal, Anzu (or Tea for viewers of the 4Kids version), a very hated character among many of the show's fanbase since she was the biggest offender of being so needlessly preachy with discussing friendship.
Overall, Yu-gi-oh: Duel Monsters pretty much has all the typical flaws you can find with an anime title being a source of product placement with its plot and characters being thinly veiled excuses to promote the trading card game that is a regular sight throughout the series. Unless you are a younger fan who also enjoys the trading card game, I wouldn't even recommend watching through the 224 episodes of this series as there is little memorable to get out of it beyond the game duels.
