Beats - the small XPs
Beats system in CoD is a replacement of the traditional World of Darkness XP system. Both of them are radically different from systems like D&D - you don't get XP for killing enemies, but for things like accomplishing goals, roleplaying, or in general - having life experiences.
In the first edition of the New World of Darkness, you would gain XP at the end of the session or story based on things like "has your character learned anything?", "did you roleplay them in an entertaining or appropriate way?", "did you perform a heroic act?", etc.
Those were a bit hard to judge at times and often felt a bit contrived. "What did I learn today? Um, let me spin the Wheel of Morality real quick and come up with something". Worst yet - the system can also feel like a further downer after a session that might've not gelled as much. I remember feeling quite shitty after playing in a session that wasn't that great to begin with and the GM sternly proclaiming at the end everyone got the minimal, 1XP. Everything else about that game has since faded from my memory, but that one thing still feels bad...
But luckily, CoD is here to solve that problem with beats! Now each XP is broken down into 5 beats, and you accrue those beats through the game through a number of concrete ways. You get a beat when you accomplish a goal you set for yourself, when you complete a condition, when you get a dramatic failure, when you risk a breaking point (essentially losing sanity or humanity), or even when you get beaten up.
All of those conditions are concrete - it is clear when they are supposed to happen and you can proudly exclaim that you are getting that beat and why. The system is much neater and feels better. However, as anything that's driven by the actions of the PCs, it can get exploited a bit...
Beat farming - stopping the game to get your numbers up
Beat farming in CoD is perhaps the last vestige of minmaxing left from the older editions of the system. You can only get one beat from a given category of beat conditions per scene, but given that you have 3-5 scenes in a session, you can rack up quite the number of beats easily.
Generally, there are a few concrete ways you can reliably get beats in the game. First two are dramatic failures and Inspired cycling. You build your character up so they have at least one very crappy roll (1-2 dice max), and then at least one roll they can use often they are very good at. Usually for the last you combine high dice number with Professional Training 2 (9-again), or Trained Observer (9-again or 8-again).
Then each scene proceed to use your weak skill until you fail, upgrading that into a dramatic failure (giving you a beat), and then using your strong skill to get an exceptional success. While exceptional successes don't get you a beat straight away, the rules state that if that check doesn't have a specific exceptional success bonus, the character should get a beneficial condition. You opt to get Inspired, a condition that you can cash in for a willpower point, a beat, and an exceptional success on 3 successes instead of 5. This means whenever you roll your strong skill, you spend a willpower point (giving you extra 3 dice), spend the Inspired condition (getting that willpower back) and fingers crossed - you get that condition back again instantly. Rinse both each scene for 2 beats per scene.
In Mage the Awakening, I'm not sure whether by design or by accident, whenever a character completes an Aspiration (their short or long term goal), they get a new Aspiration. Moreover, higher-end Mages have more and more "Obsessions" - long-term Aspirations focused on supernatural things. You can cash both an Aspiration and an Obsession each scene for a beat and an "arcane beat" (beat you can only spend on magic stuff). This can start derailing the characters into "my current aspiration is to go to where the next scene is and do what we were planning to do anyway" and "I want to learn more about the particular supernatural creature we're currently investigating". This stops being conductive to "emergent gameplay" and just becomes a race to get more and more beats...
Moreover, Mages can also farm Arcane Beats by resolving conditions imposed by spells. The book even explicitly states that farming beats this way is normal. In a sidebar section called "The Beat Goes On..." we read - "At this point, you may be wondering what’s stopping you from loading up on Condition-causing spells in a relatively safe environment, resolving them all, and earning Beats by the bucket load? The honest answer is “nothing, mages do it all the time.”...". This means if you have a Mage with Fate 2 in your party, you can cast Exceptional Luck each scene, giving everyone in the party a beneficial condition they can use and gain a beat that way.
Finally, at the end of a scene, you can just punch each other in the face and get a beat (at least if you're mortal - supernaturals might have to cut one another up for it). If you take damage in your last three health boxes, you get a beat. For an average person, you need about 5 points of bashing damage, which heals after 75 minutes - most often enough for a scene change. Punch each other in the face each scene and farm those precious beats...
So if you're hard-core, each scene you can get a beat for damage, dramatic failure, fulfilling a condition and fulfilling an aspiration rather easily. That's a beat shy of a full XP each scene, so you might end up with about 4XP at the end of a session - which is an insane amount (1XP is healthy for a normal session). Would the game be fun though? Heck no...
Mechanics distracting from the game
Discovering an exploit in a game can be fun. It makes you feel smart for noticing the various mechanics that make something up, you go through the rush of research as you dig deeper into the problem and finally you have the sense of mastery as you figure out the most optimal way of abusing the exploit. It is fun, but that's not what Chronicles of Darkness, or RPGs in general are about.
Sure, you can have a group that's all about deriving fun from breaking a game and exploiting the mechanics, do that by all means. You can similarly enjoy the Ivory Tower Game Design, but after awhile it feels like a system that punishes sub-optimal play.
Recently my group and I have switched systems in one of our game from Savage Worlds to Chronicles of Darkness. A new player joined us that didn't have experience with CoD. We had fun with the session, but by the end I came out of that session with 6 beats, and the other players had only 3 beats a piece. I am by no means a better player than them, nor was my character a more important part of that story. The only difference was I knew how to farm beats and I made a character that allowed me to farm beats. Since we're all loss-averse by nature, seeing someone get twice as many beats was most likely not a pleasant experience. We started using group beats since that point...
In a different session, one of our players cared about a particular NPC - they were tied to their backstory and so on. When my character failed a roll related to helping that NPC investigate their missing father however, I decided to cash it in for a dramatic failure and a beat, much to the dismay of the other player. The failure was not important to my character, but it was going against what the party wanted to accomplish. If we continued on this path for a longer game, we'd probably all start screwing the party over with dramatic failures sooner or later. Luckily it was a shorter game and we learned our lessons.
Cut the beats
Honestly, I feel if the beat system was cut entirely from CoD, the system might be better for it.
Say, if the players and the GM agreed to say, give everyone 1-2 full XP per session, that might be a good pace. Aspirations wouldn't give beats, but would be a way to communicate with the GM and the rest of the party what you as the player want out of a given session. Conditions already either give you a bonus when you "cash them in", or get rid of a penalty if they're negative once you get rid of them. Getting beaten up and surviving means you survived a fun action scene and either continue your story, or have some new enemy to beat up in the future. Risking a breaking point is a dramatic enough moment that it is interesting on its own, and finally for dramatic failures - perhaps the GM could offer you a Doylist choice with some kickback if they believe a botch would add to the story. Some of them could give you Willpower - another important resource in the game, or perhaps a reroll you could cash in in the future. Either of those options would be meaningful, but not important enough to heavily encourage the players to derail the game for their own benefit.
So all in all, the beats system in Chronicles of Darkness is an interesting tool, but when taken to its "rational conclusion" - it starts to break down. It's possible the game might be more enjoyable if we weren't chasing that proverbial carrot at any given opportunity...