The Piper claims he has been to many "solar systems". Only Earth's system is technically called the "solar system" (i.e., the system with the star Sol at its center).
When the group returns after escaping the Senator's home, Betty is absent for a substantial period of time during the discussion with the Piper. Where is she?
Jonathan Harris of course played the role of Dr. Smith on Lost in Space. He seems to enjoy playing the person here to offer Fitzhugh an escape, just as many weird aliens offered Smith the chance to return home if he betrayed the others on LiS. The fact that he claims Alpha Centauri is on his route may also be a nod to that series: that was the Robinson's original destination in that show, too.
In what is either a nice continuity nod or a example of el-cheapo budgeting, the music that the senator turns on to block the Piper's music is Biff's trumpet solo from the episode "Giants and All That Jazz." Apparently his music did make it big.
Fitzhugh: A wondrous portal opened wide, as if a cavern was suddenly hollowed... Kurt Kasznar quotes extensively and with great relish from Robert Browning's "The Pied Piper of Hamelin," a fairly famous literary work.