"...and quickly became an extratropical cyclone" - I'd use "quickly transitioned into an extratropical cyclone" as it transitioned into one, not originated as one, as the current wording (sort of) implies
"While active, Hazel was partially responsible for preventing Atlantic Tropical Storm Debbie from intensifying since the storm altered temperatures over Texas." - clarify which storm you say in "since the storm" - probably try using "since Hazel"
"Substantial damage was recorded in the city. Three people were reported killed in Mazatlán, two fishermen died when attempted to ride out the storm, and a boy who was electrocuted by a downed power line." - try "Substantial damage was recorded in the city — three people were killed in Mazatlán, of which two were fisherman who attempted to ride out the storm, and a boy who was electrocuted by a downed power line."
"Ironically, in 1954, a different tropical cyclone in the Atlantic Ocean, also named Hazel, resulted in the name's retirement in that basin." - didn't result in the retirement of this Hazel — remove that sentence as trivia and as it's incorrect