The sign near the entrance of the Botanical Gardens reads "Our Stamens are a Pistil". As well as referring to two parts of flowers, it is also a pun on the old-fashioned slang "pistol" meaning someone who is bright/energetic ("hot as a pistol") and thus fun to be around. The sign is thus saying (in a very obscure way) "Our flowers are fun to be around", and also explains why Lisa finds the joke hilarious whilst everybody else (including, in all likelihood, most of the audience) is just baffled by it.
As the Simpsons are entering the arboretum, one of the sculpted bushes they pass is "Binky", a character from Matt Groening's comic "Life in Hell." The other pair of bushes are Kang and Kodos, The Simpsons' resident space aliens.
When Moe tries to get out some toys, which includes a Tickle Me Elmo. After he tests some other toys, he brings out a Tickle Me Elmo. But when he thinks he abused the Tickle Me Elmo, he said "You can't tickle Elmo no more", he made the Tickle Me Elmo say "No means no for Elmo." Then Elmo slaps Moe.
Fat Tony says "I haven't cried this much since I paid to see Godfather III". Joe Mantegna , the voice of Fat Tony was IN Godfather III.
The Sumatran Century Flower is a reference to the titan arum, a massive plant with an uncanny physical resemblance and a powerful stench that has been described as ranging from "limburger cheese" to "rotting fish".
The song played when Moe is spending time with Maggie (and over the pictures of Homer and the ham) is "You're My Best Friend" by Queen. This song was later played in Dogtown when the homeless man, Rainier Wolfcastle, the elderly, Bart and Lisa reunite with their dogs at the end.