Professor Stephen Hawking mentions he has been on Star Trek and The Simpsons. He indeed appeared as a hologram of himself in Descent (1993), and voiced himself in four episodes of The Simpsons (1989). He also appeared in Futurama (1999), which was made by the creators of The Simpsons.
The remark about Penny's short hair in season 8 is probably a jab at the fact that most of Kaley Cuoco's fans didn't like her new hair style, which returned to its normal length in season 9.
Bert's full name is Bertram Kibbler.
Leonard seems to get nosebleeds from even moderate amounts of activity. Here he gets one from laughing out loud; in The Speckerman Recurrence (2011), Penny claimed that blood already pours from his nose when he jogs. In The Weekend Vortex (2012), Leonard even claimed he got a nosebleed from overthinking a dilemma.
Someone (in this case, Sheldon) finally verbally addresses the bicycle parked against the elevator on the second floor.