Yes, and he shouldn't have been--at least not in such an avenue as referencing 'sites important to Iranian culture'. It doesn't put any distance between the Islamic Republic and Iranian people or culture--and the one is not a good reflection of the other, as years of protests suppressed through shooting people demonstrate. Trump played into an Iranian propaganda piece by being overgeneral in such a way.
He was on a roll of multiple tweets anyways. Adding a few words in place of vague 'cultural centers' to suggest government facilities, state propaganda/television/whatever facilities, or what-have-you in his twitter-threat wouldn't have earned the objection. Trump didn't do that, so I'm going to object to it, because the dude needs to engage brain before jumping to twitter. Is he going to blow up the tomb of Cyrus or Qom? Almost undoubtedly no. He can take two seconds to make clear that's not the case and avoid giving the Iranian theocracy a good bit of grist for their propaganda mill--especially when the 'cost' is being more accurate and not being dumb on twitter.
Even not taking him literally and treating it as Trumpian rhetoric ala his earlier 'lets do war crimes' it's a dumb look for Trump.