Season 1 of Dragon Ball Z Abridged relied heavily on internet culture references and fourth wall gags that, while funny on their own, was love it or hate it. Starting with Season 2 and the Namek Saga, and becoming especially apparent once the Ginyu Force shows up, the dialogue become a lot wittier, relied less on fourth wall jokes and references, and had such excellent edits for the sake of jokes that if you hadn't watched the actual show in a few year you legitimately wouldn't notice a difference.
Then Team Four Star took it a step further with the Cell Arc. They had already proved their chops as excellent comedic writers, but Season 3 displayed the team's talent for writing horror and very dark humor (courtesy of the main villain) and even some tragic tearjerking scenes (History of Trunks; 16's backstory) - some fans believe that Team Four Star's writing is now even better than the Kai dub of the source material. And the production values, already excellent, took a further step - significant edits like cutting Yamcha out of an entire special for the sake of continuity, or even creating brand new animation frames.
DSBT InsaniT: Episode 5 is where characters really start being fleshed out.
The animation of Happy Tree Friends became more polished over time, while episode plots became longer and more likely to involve multiple characters. This is particularly notable in the TV episodes starting in 2006.
Homestar Runner's first major cartoons (which have since been removed from its site) were fairly awkward and at odds in characterisation with later installments. Around the point of the Fluffy Puff Commercial or Where's The Cheat, the characters started to reach their current form.
The Strong Bad Emails have almost always been the main draw for the site, and grew its beard when the show became longer and had more outdoors scenes. A decent bet would be the first Compy email "invisibility", which is a prime example of Strong Bad's Imagine Spots
I'm a Marvel... and I'm a DC began as some somewhat amusing shorts, though it relied a bit on sticking to the Mac ad series, and the stop motion was rather jarring. The series really got funny when it just picked up the concept of a dick-waving contest between the two giants and ran with it. In other words, the second RandomGuy's Green Goblin showed up.
Also on the dramatic side, it grew a dramatic beard the moment it revealed that Superman was missing, and the casual "After Hours" had suddenly become a Crisis Crossover.
Related to this was Lex Luthor and Superman's argument about erasing the Marvel universe when viewers suddenly realized the series could also be incredibly deep.
It grew the beard a second time, going from great to awesome, by adding one character - Deadpool. "Rorschach and Deadpoooooool. A nut and a fooooooooool."
The Most Popular Girls in School: While season one was definitely funny, season two and especially season three is where the show really begins to showcase its storytelling abilities and its comedy.
Neurotically Yours had very rough animation and was mostly about a squirrel rambling on about what bothered him in the world and a teenage goth girl who kept the squirrel as a pet while listening to punk music and was extremely introverted. Several episodes later, the series quickly evolved with the squirrel, Foamy, giving more coherent and thoughtful rants while also causing shenanigans. The girl, Germaine, also had her own rants and slowly shed her goth persona of the course of several years, revealing a broken and battered girl.
The series first started off as a novel concept, but all but two of the actors were amateurs, the sound was muffled and the overall pacing was slow. Season two picked things up immensely, but season three was really where Rooster Teeth got into the swing of things.
The real growing the beard moment came with the Recollection trilogy. Blood Gulch Chronicles was undoubtedly hilarious, but there were arguably just as many shows out there that were just as good if not better. Then came the Recollection trilogy with epic fight scenes, interesting plot/character development, surprisingly good acting, an awesome villain and a really gripping story, and it STILL managed to stay absolutely hilarious. All this served to finally cement Red vs Blue up there as one of the greatest Web shows of all time, with quality on the level of professionally made movies. With Season 10, Elijah Wood signed on as one of the voice actors.
RWBY has made at least three jumps in quality so far, each winning over more doubters than the last.
Episode 8 was the high point of Volume 1, delivering the show's first truly great action scene, a lot of good character development, and proof that the story was actually going somewhere.
Volume 2 started off on the right foot, with the animation, dialogue, and voice work generally better than in Vol 1, but this season gradually succumbed to very poor pacing, overuse of comic relief, and an obviously rushed, unsatisfying finale.
Now that Volume 3 has begun, it's widely agreed that this is the point where the series has truly come into its own. The animation has improved so much it's hardly recognizable as the same show, the voice work is now consistently outstanding, the pacing blows even the best episodes of the previous volumes out of the water, and the humor is much more even. The overall opinion among viewers is that RWBY now feels like a real, broadcast-quality show and not just an amateur web series. Latter half of the season contains the brutal deaths of several beloved characters and aversion of Status Quo Is God which marks a turning point in the series to a more serious show with life and death consequences.
The first two episodes of There she is!! are great, but it isn't until the third episode that the story really starts to pick up. This is mostly because, while the first two are pretty much standalone stories, the last three episodes work as a trilogy.