Factual error: When they are being kicked out of a Corpus Christi dance club in 1961 for singing do-wop, someone screams "We want to hear Tejano.". Tejano music was born in 1972 in Alice, Texas. In 1961, the correct term was "Tex-Mex" which later became "Chicano" which is now known today as "Tejano". The word "Tejano" was not known in 1961.
Factual error: The opening scene claims to take place in the Houston Astrodome, but the inside shots show that the arena has a hexagonal shape to it. The Astrodome is a circle-shape no matter what is taking place inside, and it seats about 5 times as many people as depicted in the opening shot, despite the claim that Selena's show is sold out.
Factual error: In the scene where Selena is mowing the lawn, she is wearing Fila muscle ball sneakers. Those did not come out until 1996.