I just recently completed a failure mode and effects analyses (FMEA) on a small system with very few parts. This thread topic makes me think that you're asking for only one aspect of how to look at a system. The FMEA that I was using looks at 1) The severity of what happens due to the failure, 2) How often does that failure occur, and 3) Is it easy to detect the cause of the failure before it happens?
Some failures in this game design in my opinion include the class design of the following: four elements monk, wild mage sorcerer, circle of the land druid, and the assassin rogue. Some failures of these class designs are more severe than others. The occurrence of these classes being played in my home game or in the AL games is low to very low. The ability to detect that these classes were poorly designed was fairly difficult.
Concerns with each class:
Four elements monk: This class appears to rely on a limited resource. My players of the monk had a hard time feeling like she was contributing in a meaningful way. The one time she felt like she contributed meaningfully was using shatter to collapse a tunnel. A possible solution is to utilize a rework of the Four Elements Monk that is a thread on the topic and is somewhere on the internet.
Wild Mage Sorcerer: This class does not have the versatility of a wizard in spell selection, so it's assumed that it compensates by increasing flexibility in spell casting. The player is concerned that to utilize the flexible spell casting detracts from the quantity of spells available in the day, and thus they are worse off than a wizard of the same level. A possible solution is to allow the spells per level to be 1.5x rounded down the value listed in the spells table.
Circle of the Land Druid: I haven't seen one played. I've tried to think of how to play one or mix it in with a multi-class design. I couldn't seem to make it as good as a tempest cleric or a storm sorcerer in my character concept. No possible solution has been identified a this time.
Assassin Rogue: The idea can work well depending on the game style, but the assassinate feature does not work well with dungeon dive style of game play. The other features in the class do not work very well in a game that is more focused on dungeon raiding and has very little in the line of political intrigue or espionage. A possible solution is to add a poison specialty feature to the class and rework the assassinate feature to be similar to the Battlemaster Fighter maneuvers.
Some spells that are broken are Hunters Mark and Hex. The severity of the failure is significant. The occurrence is frequent, and the detection is nearly impossible.
Concerns with spells:
Hunters Mark and Hex: My understanding of the rules on these spells is that they are intended to end if they are not moved to a creature as a bonus action before combat ends. This does not work well for the Warlock class. This may work well for the Ranger class. As the rules are written in the PH, it is easy to interpret that the spell does not end at the end of combat. A possible solution is to allow the spell to run for the full duration based on the concentration value listed.
Encounter design is broken. The severity is variable based on the player capability and expectations. The occurrence is frequent. The detection is difficult prior to running several games and receiving feedback from players.
Encounter design: 1) I believe the design intent is to use several NPC creatures in a combat to ensure there is a level of threat felt by the players. A single creature in a combat is usually overwhelmed and will die before the players feel there is a threat. Since several creatures must be used, it makes the game seem to run longer as the DM processes the actions of several creatures. 2) The encounter build tables list adjectives to describe how an encounter should feel. In many cases my players have reported they do not feel that adjective is accurate for the encounter. Therefore the DMG table provides inaccurate information. A possible solution is to design encounters based on the recommended daily XP (DRXP) value. Establish a minimum and maximum percent of that DRXP value for an encounter through testing. Test if the DRXP value listed in the DMG is accurate enough to build encounters around.
Normally, after a failure is identified and weighted by looking at the severity, occurrence, and detection values then a possible fix is identified. Assuming that fix is implemented then the severity, occurrence, and detection values are reviewed again. Hopefully the resulting value is found to lower after the fix.