Minecraft wiki entry for PC_Gamer_Demo, associated text: If the player goes to sleep in a bed and skips the night, it removes that time from their clock, decreasing their play time.
While mining, if the player opens and closes their inventory without releasing the attack key, the pickaxe does not move until they stop mining.[needs testing]
The "PC Gamer" logo can be mined. It is composed of snow blocks, red wool and black wool.
By editing the level.dat file, it's possible to change the time. Positive number means less time. Negative number means more time. Entering -999999999999999999 as time causes the demo timer to show 0:00 but the time still counts.
The demo disables the F3 Debug screen, the F8 cinematic camera, and Shift + F2 to take an extremely high resolution screenshot (a feature of retail Minecraft between Beta 1.2_2 and Beta 1.5). These are all fairly obscure and experimental features, which were likely disabled to avoid confusing new players.
The player's score (which is always 0 in the retail Beta 1.3) is not shown upon death.
Due to the developers forgetting to remove debug code, if the Demo is able to print to a log or is launched from a command line, the message "Spawnpos: (a number which is the X location that you spawn at), (a number which is the Z location that you spawn at)" is output to the log every time the player is spawned. An example of this message is "Spawnpos: 166, -57" when spawning into the demo world for the first time.
The second hint message has the old Minecraft Wiki link, at http://www.minecraftwiki.net.
The screenshots showing what other players have made that appear when the demo runs out were made by users in this reddit thread: https://www.reddit.com/r/Minecraft/comments/g2rd8/i_need_your_help_making_screenshots/