A plane appeared to bounce after landing at the Caribbean Island airport of Sint Maarten and skidding down the runway.
Authorities said one passenger was treated for burns after a seat caught fire from the burning phone. Another was reportedly injured during the evacuation.
"While they are all unrelated, I want you to know that these incidents have our attention and have sharpened our focus," United CEO Scott Kirby said.
Passengers were evacuated from a United flight at Houston's George Bush Intercontinental Airport, according to an airport spokesperson.
A Southwest Airlines passenger remains hospitalized after opening an emergency door and jumping out of the plane while it was still on the tarmac in New Orleans.
A Delta passenger describes what it was like to be stuck on that plane that reached temperatures up to 111 degrees.