Deliberate mistake: The huge bruise on Tommy's face, from the board hitting him, disappears in less than a day.
Deliberate mistake: Why would Richard, big Tom's 'right hand man,' have to drive his cherished vintage car on a business trip that would take him hundreds, if not a thousand miles? He surely could have taken a company vehicle. Of course, then they couldn't do the 'car slowly and humorously being destroyed' shtick.
Answer: In that scene, that song is followed first by "It's the End of the World as we Know It (And I Feel Fine) " (R.E.M.) and then by "Eres tú" (Mocedades). Earlier, they sing "Superstar" (The Carpenters) just before the hood flies off.