The last few weeks, I've been watching episodes from the last season of Dennis the Menace on Antenna TV. I've been struck by the number of actors who pop up on that show who would later work again with Gale Gordon on The Lucy Show. For example, there's Mary Wickes in a recurring role as Mr. Wilson's spinster neighbor, Miss Cathcart. Roy Roberts (Mr. Cheever on TLS) appears as a navy captain in one episode. Much of the action in that episode takes place aboard a ship, and is very reminiscent of the TLS episode, "Lucy and the Submarine," where he played an admiral.

Another regular is Willard Waterman as Mr. Quigley. He later showed up in two episodes of The Lucy Show: "Lucy and the Plumber" and "Lucy and the Rain Goddess." Although they never crossed paths on The Lucy Show, Charles Lane appears with Gale Gordon in an episode of Dennis the Menace that season ("The New Principal"), which was the same season he was also appearing on The Lucy Show as Mr. Barnsdahl. And this afternoon, there was an episode about a sheepdog that winds up at Mr. Wilson's house. The dog was not included in the closing credits, but it looks very much like Lord Nelson, who played Mr. Mooney's dog, Nelson, on three episodes of The Lucy Show (and later, Doris Martin's dog on The Doris Day Show).

There is another actor, George Cisar, who had a recurring role as a police officer and Mr. Wilson's nemesis. Although this actor never appeared on The Lucy Show, what's curious is that the name of his character on Dennis the Menace is Sgt. Theodore Mooney!
http://www.imdb.com/character/ch0208455/

A few other actors who appeared in the fourth season of Dennis and later on Lucy:

Bob Hastings (appeared on the Here's Lucy episode, "Lucy, the Crusader")
Jonathan Hole
Nestor Paiva

*********************UPDATE*********************
November 12, 2014: Several days ago, I was watching Dennis the Menace on AntennaTV. It was the episode "Dennis' Documentary Film." Sgt. Mooney appears in this episode and imdb.com clearly states that this character's first name is Theodore, as in Theodore Mooney, just like the character on The Lucy Show:

http://www.imdb.com/title/tt0557928/

However, this is WRONG. During the presentation of the documentary film, Sgt. Mooney is introduced as Sgt. Harold Mooney. His name is NOT Theodore.

You forgot Dennis himself, Jay North! He appeared on TLS in the fourth season playing Mr. Mooney's nephew!

Elvia Almann, Parley Baer and Harvey Korman appeared on both shows, also.

And the other Mr. Wilson, Joseph Kearn, appeared on I Love Lucy, as the theatre manager. So, both Mr. Wilsons were on ILL.

And another Lucy/Dennis connection, Katherine Card, who played Lucy's mother on ILL, appeared as a woman standing in front of the drug store on DTM!

You forgot Dennis himself, Jay North! He appeared on TLS in the fourth season playing Mr. Mooney's nephew!

Elvia Almann, Parley Baer and Harvey Korman appeared on both shows, also.

Of course, yes, I meant also to include Jay North. Good catch on the other three. But did Parley Baer actually appear in any DTM episodes during the Gale Gordon era? I know he was on there earlier on.

And the other Mr. Wilson, Joseph Kearn, appeared on I Love Lucy, as the theatre manager. So, both Mr. Wilsons were on ILL.

Actually, I think it's even more ironic than that. If you expand the Mr. Wilson character to also include those who filled in after Joseph Kearns died and before Gale Gordon arrived, then that would include Willard Waterman and Edward Everett Horton. Willard Waterman, who played Mr. Quigley, assumed the Mr. Wilson role in the very first episode after Kearns' death. I don't mean he played Mr. Wilson, but in the character of Mr. Quigley, he was given the Mr. Wilson lines. And then in the next episode, Edward Everett Horton assumed that role in the persona of Martha Wilson's uncle. And, of course, Joseph Kearns, Gale Gordon and Edward Everett Horton all appeared on I Love Lucy during its first season. Willard Waterman never appeared on I Love Lucy, although he did appear twice on The Lucy Show.

And another Lucy/Dennis connection, Katherine Card, who played Lucy's mother on ILL, appeared as a woman standing in front of the drug store on DTM!

I didn't know that. :)

There is another actor, George Cisar, who had a recurring role as a police officer and Mr. Wilson's nemesis. Although this actor never appeared on The Lucy Show, what's curious is that the name of his character on Dennis the Menace is Sgt. Theodore Mooney!
http://www.imdb.com/character/ch0208455/

Several days ago, I was watching Dennis the Menace on AntennaTV. It was the episode "Dennis' Documentary Film." Sgt. Mooney appears in this episode and imdb.com clearly states that this character's first name is Theodore, as in Theodore Mooney, just like the character on The Lucy Show:

http://www.imdb.com/title/tt0557928/

However, this is WRONG. During the presentation of the documentary film, Sgt. Mooney is introduced as Sgt. Harold Mooney. His name is NOT Theodore.

And the other Mr. Wilson, Joseph Kearn, appeared on I Love Lucy, as the theatre manager. So, both Mr. Wilsons were on ILL.

And another Lucy/Dennis connection, Katherine Card, who played Lucy's mother on ILL, appeared as a woman standing in front of the drug store on DTM!
didn't Joseph Kearns also play the owner of the nightclub where Ricky worked on I LOVE LUCY once?

didn't Joseph Kearns also play the owner of the nightclub where Ricky worked on I LOVE LUCY once?

No, Joseph Kearns played a psychiatrist. Gale Gordon played the owner of the Tropicana -- twice.

that's right; now I remember! (I haven't seen ILL in YEARS; since it was on Nick at Nite)

Joseph Kearns also played the theatre usher, when The Ricardos and Mertzes go to the theatre.