Bridge: Oh, yeah, well...long story short, our mentor, who's a dog, got promoted to head of SPD, which used to be run by a bird, but he retired and went down to Miami, and then Sky got promoted, and then I got promoted, and that's why I'm the Red Ranger...or rather will be.
Made better by how the camera cuts to everyone else's faces while he's rambling: Xander and Tori look amused, Kira looks like she's experiencing deja vu, and Adam gives Bridge a look of quiet concern. Dax has an expression of bemused delight on his face, while Will and Rose are clearly skeptical. Ronny is trying hard not to laugh and poor Mack's at a complete loss for words. It's strangely fitting that it's Dax who says this to Bridge:
Dax: Makes sense to me.
Adam sums up what every long time fan thought when they first watched Dino Thunder:
Kira: Dr. O would've loved to see that.
Adam: Hey, you know, I still can't believe he's a doctor.
Apparently, Johnny Yong Bosch wanted to get out of having Adam say "Morphenomenal," and he was vetoed.
At the end of the second part, after the battle is won and the Rangers are hanging at the mansion, the writers managed to put in one last nod to SPD. Spencer walks in with a stack of toast for Bridge, and this exchange happens:
Bridge: Is it... *makes his little hand motion*
Spencer: ...The butteriest, sir. *also does the little motion*
In one episode, Flurious says he has half a mind to turn Norg into a throw rug, and later says he has half a mind to shave him until he resembles a naked ice rat.
Norg: Half a mind... for a throw rug... half a mind, naked ice rat—Well, that only leaves one half left! Flurious: FIIIIIIIND MYYYYYY JEWWWWWWWWWWWELS!
In "Follow the Ranger", we get a brief glimpse into the past of Moltor and Flurious. Apparently they first started hating each other when Flurious broke Moltor's red sled as a kid.
And when they start fighting each other at the very end, Norg is standing watching on the side just muttering, "Here We Go Again", and cringing at the off screen violence.
In "Both Sides Now": "...Man law."
For context: Will has defected to join Miratrix, and Dax is venting about how you don't just hook up with your friend's ex. When Rose and Ronny turn around, he and Mack have their shoulders on each other and they say the above line at the same time (a lot of us know that as "bro code", but still).