To the iM@S games:

Kyoji holds a magazine with 765PRO ALLSTARS on the cover in his two initial cards.
Minori is a long time idol-fan, but his favorite unit is Ryuuguu Komachi. His design could also be a shoutout to one of their members; see his page for details.
Ritsuko appears in the pre-changed version of Ryo's Remember Shot card.
Yumeko, Ryo's rival in his story of Dearly Stars, appears in his initial SR card before change. Ai and Eri also show up in his Candid Shot card.

To other series:

Pierre carries around a Don-chan plush in one festival card.
These◊ cards◊ surely give us a Psycho-Pass flashback.
The clocks on Legenders' initial R+ cards kind of resemble the artwork of a certain, kind of eccentric artist.
- Especially Amehiko's Print.
- All the Legenders members themselves (along with the rest of the Idol Discovery Project candidates) are based on historical figures. Amehiko is based on Abe No Seimei, Chris on Christopher Columbus and Sora on Matsuo Basho.
One of the events, Ghost Snipers, is a giant pastiche of Ghostbusters.
The event Write for someone ~A Reminiscent Sky~ takes some stylistic cues from Night on the Galactic Railroad. Mitsumasa, Sora's character, wears a cape lined with railroad cars and stars.
The Hot-Blooded Reasoner TALK&LIVE event has Jupiter and Legenders promoting their theme song for a popular robot anime. Their outfits highly resemble a certain mecha anime, too...
Guardians of Sanctuary ingame is a big homage to Dungeons & Dragons, being a popular tabletop RPG that the idols themselves play.
One of Shiro's favorite card games, Beast Chronicle, is a reference to either Yu-Gi-Oh or Cardfight!! Vanguard. The theme song for Beast Chronicle ~Risin' Soul even sounds like an open taken directly from one of their animes!