When Kurt sits at the piano to play "I'll Stand By You" for Finn, he is wearing light-colored pants. When there is a close-up of "his" hands playing, the person playing is wearing jeans.
When Suzy Pepper eats the world's hottest pepper (after Will lets her know they'll never be a couple), a strand of hair can be seen in her mouth. Then the strand disappears on side shots, but reappears in her mouth when she finally chomps on the pepper that burns out her esophagus. (About 10 minutes into the show.)
When Kurt encourages Finn to sing his ballad to his baby, he sits down at the piano to play. He's wearing brown leggings, but when they scan to his hands playing the song, blue jeans are visible for an extended time.
The world's hottest pepper isn't from Mexico, it's from Trinidad and Tobago - the Trinidad Moruga Scorpion. Further, "hot" peppers don't literally burn and will not "burn" holes in organs. Rather, create the sensation of burning.
Kurt tells Finn his mom died ten years ago, but as a sophomore, he's only 16. Other, later dialogue indicates that Kurt was 8 when his mom died.