When Gina is talking to Michael about his friends, she mentions an 'Asian kid who's allergic to light'. This is a real, and extrememly rare, condition known as xeroderma pigmentosum.
On Joey's Magna Doodle: A goat eating out of a garbage can in front of the Hollywood sign.
Goof: Just after the opening credits, when Joey runs out to see Jake, Jake has one hand out in one shot and then puts the basketball in both hands. When the shot changes, his hand is out again and then he puts the basketball in both hands again.
Time Index 21:12. Joey and Gina had left Michael at the bar and come back to the apartment. The scene took place in the evening but you can clearly see that it is daylight through the window in the background.
Gina mocks Joey by saying his pick up line, 'How you doin?' over and over. Joey then replies that it worked on all of her friends. However, it is revealed in season one episodes 8 and 9 (Joey and the Dream Girl Parts 1 and 2) that Joey was always awkward around Gina's best friend Donna (played by Kelly Preston) and that though he had a huge crush on her, he never slept with her.
Time Index 8:24 and a few seconds after. Joey can be seen playing with his Rock'em Sock'em Robots set. This is the same set that he and Phoebe played with on Friends. Many of the props from Friends (like the magna doodle) were brought along and worked into the setting to foster familiarity.
It is revealed that Joey was 11 the first time he went to a bar to pick up a girl.
Gina says that she made a bunch of keys after Joey turned down 'that hit show' because she thought he might kill himself. The show she is referring to is Nurses. It was learned in the Pilot episode that he turned the show down for a bloody cop drama. His show ended up getting cancelled and Nurses became a huge hit overnight.
On Joey's Magna Doodle: During the first half, a bird that looks like a phoenix rising from the fire/ashes. Near the end, a power lifter lifting a heavily weighted barbell.
"Take Me Out" by Franz Ferdinand
Goof: During the scene when Joey and Michael go to Gina's after she got them kicked out of the bar, the cork in the wine bottle appears and disappears from the bottle.
Gina is actually the first one in this show to use Joey's famous line 'How you doin?'.
It is revealed that Michael is 20 years old. Gina tells him that she had him when she was 22, though Joey later reveals that Gina was 16 when she gave birth to Michael. That makes Gina 36 years old.
Michael is a rocket scientist, having graduated from Caltech.
Gina is a hairdresser, which she only started doing because she was exposed as the Southland's most dangerous dental technician.
Alex is a corporate lawyer.
Joey's Magna Doodle wasn't up in this episode because the movers hadn't arrived.
"Hooray For Hollywood" by Johnny Mercer
Goof: In the scene where Joey and Gina are on Joey's new apartment terrace, looking at the Hollywood sign, the strings dangling from Gina's chest keep going into her sweater and dangling out of it.
Goof: In the scene after the introduction, when Joey and Gina are at the airport, Joey's bag strap at one point is under his collar, then when the shot changes his collar is under his strap. This mistake keeps happening during this whole airport scene.
It's revealed that Alex's full name is Alexis Julia Garrett.
Goof: When sitting by the pool, Gina's feet are black (because she was walking without any slippers). However, a second later her feet are already clean.