Base-Breaking Character: Natsuki. You may like her for having an interesting character arc and her cute appearance provided by Chise Nakamura or hate her for doing many dumb things that may even endanger her own team.
Bizarro Episode: The aforementioned Task 39, coupled with Clip Shows of past episodes (first as they try to figure out which villain sent them the Prometheus Stone, then when its bomb is accidentally activated and everyone decides to stay together when it goes off). As it turns out, it was Makino-sensei who gave them the Stone as a form of training, and they stopped the bomb in the nick of time by smothering the Stone in Aegean salt. That is, no henshin, no mecha fights, and Eiji and Masumi dancing hula among other things.
Broken Base: The suits. Are they the most awesome thing ever, or way too cluttered and ugly?
Fridge Brilliance: Natsuki/Bouken Yellow being a Lemurian Princess would look normal, unless you realize that back then in Dai Sentai Goggle Five, Lemuria is the civilization symbolized by Goggle Yellow.
In Task 22, several members of the team (Masumi, Natsuki, and Satoru) are transformed into different animals. Masumi is... A German Shepherd. However, this actually makes a lot of sense; Shepherds are favoured as police and army dogs, and are generally considered dangerous and aggressive. In reality, however, they are actually quite intelligent, friendly, and loyal—quite bit like Masumi himself. He comes across as the mean 'bad boy' of the group, but actually cares quite a lot about the team, and is much nicer than he originally gives himself out to be.
Unless their numbers are being multiplied by special effects, you only seem to see a maximum of three Jaryuu on the screen at once, much like Land of the Lost, where you only saw three Sleestacks on camera at once because that's how many costumes they could afford.
Episode 35 gives us a version of Momotarou. The Kamen Riderseason that would air after Boukenger gave us a new twist on the concept.
This ended up happening again in the next anniversary series with the Sugormin, except in this case, it was because Toei only made 3 costumes as opposed to just not being able to afford more.
On the topic of Gokaiger, AkaReds gimmick of transforming into past Reds ends up being a precursor to the Gokai Change, where the Gokaigers can become past Rangers.
Memetic Mutation: Let's just say Masumi is better remembered by his crooked teeth than by his actions.
They Wasted a Perfectly Good Plot: A couple episodes imply that the SGS doesn't fully trust the Boukengers and may be hiding things from them. This leads to... absolutely nothing.
What an Idiot!: Gaja decides to revive the Ashu as the Questers, and he didn't even come up with a plan to keep them from turning on him.