This is sort of a "mission statement" of how I design and review content. It isn't the only way, but it is my way. These statements are not concrete, objective truths of design, and I'll probably revise this over time.
It is hard to pin down any kind of objective measure of game design, especially in a tabletop context. In the context of D&D 5e, I choose to generally peg Wizards of the Coast's official releases as a general baseline, and more specifically the Player's Handbook. These act as my reference points for formatting, wording, design, and balance. These are not perfect reference points, as I have lost trust in Wizards' design over time as they have released what I consider to be various poorly designed things into the game. Even the Player's Handbook itself has multiple relatively glaring piece of poor design contained within. Yet, it is the foundation of the game, that which all else must be compared.
I can sort of group my thoughts into three primary categories: Congruence, Elegance, and Balance, though each overlaps with the others in various aspects.
Congruence
One of the very first things I notice when I read a piece of content is, how well does it seem to fit into existing content. Does it operate and is worded like official content? Is it laid out in a familiar manner with clear formatting? Do the ideas seem to match the general fantasy of D&D? My gold standard for this is that I should beable to staple the content into the Player's Handbook and it will blend in nicely (trade dress aside).
Some parts of this are less important in some contexts. For instance, with setting-specific content, matching the flavor and tone of the Player's Handbook is usually not much of a concern, even if matching its wording and mechanics is still important. I wouldn't expect a science fiction race to blend into the Player's Handbook, but I would still expect it to be formatted, designed, and written like other 5e races.
The most obvious example of problems in this area is in wording, take this sample:
Using your standard action your sword becomes a +1 weapon with +2d8 fire damage for 5 turns.
You can basically understand what this feature is saying, but it does not at all read like 5e language. "standard action" is a holdover from earlier editions that 5e doesn't use (I see this kind of wording mistake a lot) and "5 turns" especially is not a duration 5e would use (does it even mean turns or does the writer mean rounds?). A proper 5e writing of this feature would look more like this:
As an action you can cause a weapon you're holding to envelope in flames for 1 minute. For the duration, the weapon becomes magical, you gain a +1 bonus to attack and damage rolls with it, and it deals an additional 2d8 fire damage to any target it hits.
Typically 5e is rather direct and verbose about what a feature does. You don't need to know the background of what a "+1 weapon" does, the feature just tells you. 1 minute is 5e's standard duration for "basically a whole combat", and 5 rounds is basically that, so there's no real mechanical difference being made there.
You might be able to use the first example, but it clashes with how other things are written in the system, causing some mental overhead to "translate" when in use. The second example is direct and clear, removing that potential problem. Ease of Use is one of the primary goals of good 5e design and this kind of clear, congruent wording helps players of all experience levels read and understand the content.
Elegance
One of the big shifts from 3.5/4e into 5e was a refocusing on elegance over complexity. 5e No longer throws around floating modifiers and obtuse mechanics to achieve its goals, instead it uses clear mechanics and understandable math, and this is a quality that I search for in additional content. Does it use simplicity when possible, instead of allow unnecessary complexity to creep in through design? Does it use existing parts of the system to its advantage instead of creating new systems where they're not needed? Does it strive to accomplish a thematic goal rather than simply try and add more crunch to the game? My gold standard for this is that I should beable to show it to new players and it should be easy to explain and use, requiring no advanced math or high-level understanding of mechanical conceits.
Sometimes complexity is warranted and good, but avoid deploying it pointlessly and clumsily. A mechanic can be both complex and elegant, it just requires the right design. For example, take the following feature:
While in your Rage, your Strength and Constitution scores both increase by 4, to a maximum of 30. This bonus increases as you gain levels in this class. You can also gain the benefits of the Great Weapon Master feat.
On the surface, this doesn't seem very complex, but when you try and figure out what the feature actually does, you have to go look at other parts of the rules to find out. You have to recalculate your Strength and Constitution based bonuses everywhere on your character sheet for this temporary bonus, which is a serious pain. Not only that, but then the feature references a feat elsewhere in the book that you then have to look up! This is an inelegant feature, compared to the actual way Rage was implemented in the Player's Handbook:
While raging, you gain the following benefits if you aren’t wearing heavy armor: You have advantage on Strength checks and Strength saving throws. When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table. You have resistance to bludgeoning, piercing, and slashing damage.
This does assume that you know what "advantage" and "resistance" mean, but those are core game mechanics used by all characters, and it does make you go reference your class table, but it's right there on the same page. No recalculation of bonuses, just a simple + to damage and advantage on rolls. No bonus to hitpoints, just resistance. This is much more elegant than the previous incarnation of Rage, making it much easier to use and clearer as to what its bonuses actually do. In design it is also much more tweakable as you have direct control as the designer over the bonuses granted, instead of relying on secondary game mechanics like feats.
Balance
Balance is basically a buzzword, but I think it does actually have a meaning and is very important to the game, at least in how I view things. Balance is the comparison between different options in the game content, primarily stuff like race, class, subclass, spells, feats, etc. "True balance" where everything is exactly the same power level is not particularly feasible, so I strive for a "within acceptable bounds" approach. Does it overshadow or obsolete existing content? Does it break 5e math such as Bounded Accuracy? Is it is too versatile or powerful for the level it's gained? How does it compare in power and versatility to similar components of the system, other races, other classes, other subclasses, other spells, etc.? My gold standard for this is that I should beable to drop the piece of content into any random game with an unsuspecting DM, and it shouldn't cause problems in a general case.
Balance is contextual. In a game set underwater, a swimming speed is much more useful than a game set entirely in a desert. An optimized, tactically-minded player is going to use their class features to greater effect than one who doesn't pay much attention. I consider balance in the General Case, across a spectrum of contexts. Things can certainly be situationally useful, but ideally not dominantly so in that situation.
In some contexts, the baseline of balance is different. Magic Items tend to be direct upgrades to the players power level, separate from the normal balance of classes, but knowing for instance, how a set of magic items are balanced against each other, can be quite useful. A 1st level spell should obviously be weaker than a 9th level spell, so the comparison point instead becomes between spells of the same level, and across class spells lists. For instance, take this spell:
Healing Ritual. Level 2. Casting Time 1 minute. Range 30 feet. Up to six creatures of your choice that you can see within range each regain hitpoints equal to 10d6.
Hm, that seems like a lot of healing, how much healing does a similar healing spell from the Player's Handbook provide at that spell level?
Prayer of Healing. Level 2. Casting Time 10 minutes. Range 30 feet. Up to six creatures of your choice that you can see within range each regain hit points equal to 2d8 + your spellcasting ability modifier.
That is much less healing than the new spell Healing Ritual provides, making it basically pointless in comparison. This is a clear sign of imbalance, if new content is power creeping on the old, leaving it completely in the dust. There are many cases of games where this kind of design is allowed to run free, and you end up with an arms race of new books and content needing to 1-up the old, and you get a game system filled with useless detritus that has been obsoleted by newer books (hope you have the cash to buy them). It also makes a player with Prayer of Healing seem weak compared to one with Healing Ritual, and if they're in a party together that is just not a good time.
To me one of the great benefits of balance is that if the game system is level, the players can do as they like within it. Trap options make players feel bad for picking things that seem cool to them, and power creep is the process of creating trap options. When there is balance, there is more diversity in characters, as there is no mechanical pressure to pick this race or not pick that subclass because they're too strong not to pick, or too weak to meaningfully contribute. For me, the lack of balance in a game system saps it of its possibilities, and of its fun.
There are of course more elements than these three to any piece of content, but these are the primary criteria that I use in my thought processes. Ideally a given thing is also fun and engaging and interesting and evocative, as well as well-presented and organized and all sorts of other good qualities, but a lot of that becomes very context-sensitive and less generalization. What one person thinks is fun and cool another thinks is boring and dumb. What's good organization in one product is ill-fitting to another. These three principles are what I'd call higher-level design thoughts, a great big Lens that colors everything that I look at.
There are also other contexts and lenses than mine out there. There are people who say things like, "Balance is impossible, don't even try." or "Why should I stay within 5e design when I am a 3rd party designer, I'm not Wizards.", and those may be valid, but they're not viewpoints that I share.