Note: I have not tested these commands yet. This information comes from reading the code and my blurry memories.

"exit" or "quit" - Closes console
"h" or "help" - Show an incomplete list of commands
"deviceinfo" - Shows your device name, type, shader level and VRAM.
"giveroomkey" - Gives you the key to the Kai Tak hotel room (not sure if master key or not)
"clearcache" - Resets user settings
"deleteallsaves" - Obvious
"togglemustache" or "togglemoustache" - Toggles facial hair
"givelaughgun" - Give a "laugh gun". Not sure what that is since I can't test these right now.
"noexit" - Toggles a variable called "noexit". Not sure what that does.
"givepheromone" - Probably gives the player the bird perfume.
"giveswatter" - Gives the player the fly swatter.
"weddingqake", "weddingquake" or "wedding" - Starts Wedding Qake
"carfighter" - Starts car fight minigame.
"unlocktv" - Unlocks TV Man in Wedding Qake
"unlockpredator" - Unlocks the homeless man in Wedding Qake.
"rec" - Sets the game into trailer recording mode (not sure what this does).
"nobots" - Turns off bots in Wedding Qake.
"giveukelele" - Gives the player the ukulele (doesn't work apparently).
"givedegausser" - Gives the player the degausser.
"siren" - Puts police sirens on screen (not sure about this one).
"givepackage" - Gives the player the package for the pigeon quest.
"cough" - Not sure, probably coughs.
"norest" - Likely disables the rendering of the sushi restaurant.
"gorest" - Probably teleports the player to the sushi restaurant.
"nopred" - Disables the "predator scenario".
"ego" - A test command for the Editor's ego meter.
"labtest" - Teleports the player to somewhere in the Soviet lab.
"allfood" - Dumps food on the ground.
"impulse101" - Dumps weapons on the ground.
"load puppetSubway" - Does nothing, but was probably used for the "director puppet".
"puppetmode" - Does nothing, but was probably used for the "director puppet".
"mic off" - Disables the puppet mic (?)
"hi" or "hello" - Makes the console say something.
"fps" - Toggles an FPS counter.
"riftmode" - Does nothing, but implies that there was VR support at some point in development.
"screensaver" - Shows a screensaver of some kind.
"clip" - Disables noclip.
"noclip" - Toggles noclip (making "clip" pointless).
"fnc" - Toggles noclip, but increases the noclip movement speed.
"iddqd" or "godmode" - Toggles god mode (probably affects Wedding Qake).
"atheistmode" - Disables god mode (useless since "iddqd" and "godmode" are toggles).
"clearachievements" - Removes all Jazzpunk achievements (don't know if this actually works).
"deferred" - Enables deferred lighting.
"forward" - Enables forward lighting.
"ul" or "allchap" or "unlocklevels" - Unlocks all chapters on the chapter select screen.
"locklevels" - Locks all chapters on the chapter select screen.
"uc" or "allchar" or "unlockcharacters" - Unlocks all Wedding Qake characters.
"resetgame" - Resets everything.
"walkfast" - Walk fast.
"graduate" - Does nothing (maybe it did something in the first version?)
"sharewaremode" or "demomode" - Enables demo mode (probably used when demoing the game at E3 and similar).
"antialias" - Toggles anti-aliasing.
"giveruscartridge" - Gives the player the data cartridge.
"give turtle" - Turtle :)
"give turtle left" - Turtle :), but in left hand.
"give tube" - Puts a vacuum tube in the player's hand.
"give brain" - Puts a brain in the player's hand.
"give degausser" - Puts a (cosmetic) degausser in the player's hand.
"give cartridge" - Puts a (cosmetic) data cartridge in the player's hand.
"esh" - Gives the player scissor hands (?).
"give spider" - Puts a spider in the player's hand.
"allspid" - Gives the player all the spiders.
"give radio" - Puts a watermelon radio in the player's hand.
"give kidney" - Gives the player a kidney.
"explo" - Tries to load the level "thunderbirds", but that level doesn't exist.
"setup don bar" - Sets up the tiki bar like in the trailer.
"setup don cars" - Sets up the BP hover cars like in the trailer.
"airport" - Tries to load the airport for the trailer, but the level doesn't exist. It does exist in the first version though.
"setup don alley" - Sets up the alley like in the trailer.
"lockheight" - Prevents the player's height from changing.
"unlockheight" - Undoes "lockheight".
"set fps 30" - Sets the target framerate to 30.
"set fps 60" - Sets the target framerate to 60.
"set fps 100" - Sets the target framerate to 100.
"textadventure" - A spoof of Zork.
"riftreticle" - More remains of the scrapped VR mode.
"2p" - Sets up a two player game of Wedding Qake.