There were some other references in Newhart's 80's show to his 70's show. There was an episode where Jack Riley (Elliott Carlin in the 70's show) was a guest at the inn and he made a remark about a crazy psychologist in Chicago. There was also a scene where Dick Loudon (Newhart) said he was watching his favorite TV show, and the theme music from his 70's show started playing.
Another show in which Riley appeared as Carlin was another MTM show, St. Elsewhere. He was a patient in the mental ward with Oliver Clark (who had played another Newhart patient Mr. Herd). In the show, Clark plays a John Doe who thinks he's Mary Richards from MTM and goes around referencing other characters. What makes the bit really memorable is (at 37: 30 below) Betty White is playing a bureaucrat who Clark insists is Sue Ann Nivens, but she claims it's mistaken identity. Roughly eight minutes into the show Carlin and Clark's character are watching TV, with Carlin wanting to watch The White Shadow--yet another MTM show:
NOTE: The picture is smaller and audio speeded up, but it's still worth watching:
https://www.youtube.com/watch?v=m6jrll0L-U4
On an episode of All in the Family, Edith makes a comment about Perry Mason vigorously offering an objection by quickly rising to his feet, She then says (with a nod to Ironside), "He don't jump up no more."
A Gilligan's Island episode made a reference to Dr. Kildare.
On Michael Learned's post-Waltons series, Nurse, there were some Three Stooges fans on the crew. One episode, had regular interplay while the PA put out a call for "Dr. Howard, Dr. Fine, Dr. Howard."
Not really another TV show, but there was an inside joke on Chicago Hope connected to one of the show's stars. Christine Lahti. She had just won an Oscar and her character was battling with a patient who was offering phony boasts about what he'd do, and she replied, "Yeah, and I might win an Oscar."
Batman and Green Hornet had the same producer, so one scene on each show had Bruce and Dick watching Hornet and Britt and Kato watching Batman. The start of Batman's second season had cameos plugging four different new ABC shows. Both Milton Berle and Phyllis Diller appeared, though neither of their characters was connected to their actual show. However, one window cameo had Hornet and Kato (who apparently became villains months later, LOL), while another had Howard Duff as his character Sam Stone on Felony Squad.
On Mad Men (circa 1967), Don Draper's second wife either gets a role or is up for one on Dark Shadows. This episode (which doesn't mention DS by name, but it's pretty obvious) appeared at about the time the big-screen version came out, so I'm sure this was effectively product placement.
In another episode, Don Draper comes home in October 1968 and flips on a Dragnet episode where Joe Friday is hosting Bill Gannon and wife at his apartment. The fact that the Dragnet ep in question matches the time frame for the episode wasn't coincidence--Mad Men viewers were sticklers for spotting anachronisms and griping about it.
Antenna TV has a current promo commercial that shows some of their programs doing this, including Maude referencing The Partridge Family.