Continuity mistake: In the opening of the movie, when Rusty and Danny are flying back to visit Rueben, you see them boarding a Gulfstream G200. However, the interior shots actually show them flying in a Gulfstream 5 (probably the one on the ramp next to the G200 when they exit the aircraft).
Continuity mistake: While the group talks about the plan to flirt with Sponder, Linus snaps his fingers and the position of his arm swaps from being up to being at waist level from one frame to the other when the angle changes.
Continuity mistake: While talking about the plan to flirt with Sponder, Yen's head swaps brusquely positions between shots.
Continuity mistake: While Reuben is in bed, the tissue paper on the night table changes positions between shots.
Continuity mistake: When Rusty is in Bank's office posing as a seismologist, Bank's glasses appear, disappear, then reappear between shots.
Continuity mistake: When the system is rebooting, during a camera pan across one of the craps tables, the printed graphics on the felt are reversed and backwards indicating the film was likely reversed to keep the direction of motion.
Answer: Linus was trying very hard in all three movies to prove himself to Danny, Rusty, and his parents. The nose is obviously his innovation, and he wants to show that it's a great disguise entirely of his own creation... even though it's pretty obviously superfluous, as it seems that no one recognizes him anyhow.