The Professor throws away a Motorola DynaTAC, probably the "8000X" model from 1983.
The boil on Leela's thigh was named after Susan Boyle.
The eyePhone is an obvious reference to Apple's iPhone.
Judging from the perspective of the video of Leela flying through the ship's window onto the table, Hermes was the one who uploaded the video.
In the zombie parade there is a clown who bears similarities with Krusty from The Simpsons. Also, the goat (Mr. Chunks) from this episode also appeared in The Simpsons as statue, in the episode "She Used to Be My Girl". (Season 16, Ep. 4)
Amy's mini-cellphone makes another appearance in this episode.
While "online", Fry states "I feel like a mindless zombie!" This is foreshadowing the end of the episode, when Mom enslaves between one million and two million people, turning them into mindless, product hungry, zombies.
In the episode, Bender mentions August 6th, 1991. This was the date the internet was made public to everyone.
When the crew go to the Third World of the Antares System, the crew learns that all labor (except the whipping) is done by children. However, when they first arrived, adults stripped down the ship and Bender. This may have been ignored to not ruin continuity by prematurely showing the planet's children as workers.
When Mom activates the "Twitworm", every character seems to be affected except Fry and Bender, who were unwittingly sending the "Twitworm" through their eyePhones. Leela wasn't affected by the "Twitworm" since she stopped following Fry's Twits earlier in the episode.
The other possibility is that robots cannot be affected by the "Twitworm," and that Fry is missing a delta wave.
Mom's eyePhone application "Twitcher" is an obvious reference to the very popular social networking site "Twitter". Also, the posts on Twitter are called tweets while the posts on Twitcher are called twits.
The way that Professor exploded Soda and Mentos is impossible to do in real life.
When Leela calls Fry, the darkness outside indicated that Leela was in space, but seconds later she is on Earth flying at a low speed.
When Fry records Susan in his eyePhone, the viewer can see "REC*" in the eyePhone display, which should be displayed mirrored since the phone is turned to him and we are seeing the back of the display.
When a character sends a Twit, it appears to be received sequentially (i.e., one at a time) by his or her followers, which shoudn't happen because every person on-line should receive the message at the same time.
In "The Late Philip J. Fry", the scene where the group is sitting in the table is seen when Bender, Fry and the Professor are traveling in time, and just before the professor says: "One year to go", implying that this episode happens one year before the events of this episode.
Fry's line "Shut up and take my money!", has become a popular internet meme.
Some memes even have Fry dressed as a popular fictional character giving away different items.
The stripping of the Planet Express Ship at an unsafe, ecologically unsound worksite is a reference to the "shipyards" at Alang where old ocean going vessels are dismantled by hand.
