That's actually just a bug in the labels not getting updated, it does clear out the conflicts it just doesn't update the label on the conflicted button to show its no longer bound to that. Internally its a 'bind as many as you want, we'll remove old conflicts' system rather than a 'finite slots' system so that you can, say, bind QWEASDZXC as left and UIOJKLM<> as right if you have difficulty pressing a specific key and want to make whole regions of your keyboard be left / right / jump. You can just refresh the page if you bound a whole bunch of buttons unintentionally.
Yes, the physics took a hard right turn halfway through development and we didn't get them polished to what we wanted in time for the deadline. There's a post-jam patch ready to go that addresses the slippery movement, hard landings and the all-or-nothing jumps. (Similarly, hitting ui_back to exit a level or exit the campfire scene early just didn't make the deadline, its in our 1.1 patch)