As her career progresses, it seems that Zsa Zsa Gabor played herself more often than fictional characters, and that was the case here.
Ernie, left alone for the day, decides to go exploring on his bike in the Hollywood Hills. Eventually afoot, he falls down a hill into a swimming pool ... Zsa Zsa's as it turns out. Uncle Charlie goes looking for Ernie, and Tramp leads him to Ernie's abandoned bike. Confusion ensues as Ernie can't reach anyone by phone, and eventually a search for him is commenced in the hills.
I found this episode of interest as several geographic clues are provided. I assume they are without accuracy, but let's pretend it's real, for fun.
1. Uncle Charlie reports that Ernie "crossed north of Sunset".
2. Ernie is in hills, looking down on a valley with expensive homes.
3. Zsa Zsa says "I knew I built my pool too close to the retaining wall."
Now, if Ernie headed straight for the hills from the south, crossing Sunset, that likely puts the Douglas house in West Hollywood.
There are three canyons in that area that have homes built along them. Examining the homes and streets with Google Maps, I can see only one home that really fits the definition of having a pool right up to a retaining wall. That house is on N Curson Ave.
Earlier in the season, there were scenes at the home of Katie's family in the area, and they were in Glendale. It seemed only a short trip from the Douglas house, which could also confirm West Hollywood.
Of course, we'll never find the Douglas house, since it was just a facade on the studio back lot. LOL
At least their house in California isn't a magic moving house like their original home in the Midwest (which was a few hours train ride outside of Chicago, and near both major airport and an Air National Guard airfield). The house in the Midwest, in the opening shot, was set back from the street with the driveway on the left. During the show, it was right off the sidewalk, with the driveway on the right.