Continuity mistake: When America and Wong jump through the Star Portal just before Wanda destroys Mount Wundagore, you can see they will travel to Kamar-Taj. However, when America opens another Star Portal to retrieve Dr. Strange from the destroyed universe, they are standing back on the snowy mountain top.
Suggested correction: If these moments were back-to-back, this may be a mistake. Problem is, there is quite a gap of time that passes between the two scenes... as in, almost 5 minutes of screen time, which might translate to even more time in-movie, as we don't know how long Strange waits to wake up Palmer, who is passed out when the scene cuts back to them. It's entirely possible and even likely that they returned to the mountain top in the meantime to see if they could find any traces of Wanda.
Continuity mistake: At the wedding, Christine tells Stephen something quite hurtful; wide-eyed, he asks her how long did she have it in the barrel; a black partygoer walks behind him but is gone in the reverse shot. Moreover, she replies "Long time" and a couple walks past her, only to walk again past Stephen in the next shot.
Continuity mistake: When the hero of the movie savagely tortures for weeks a guy who dared to touch his mantle after being robbed, the mustard on Bruce Campbell's clothes changes position from shot to shot.
Continuity mistake: Stephen performs a magic trick very popular at weddings a couple millennia ago changing water into wine; as he does that, you can notice that the barman in close-up is bent over behind the counter, but he was standing a moment before when Strange started the gesture.
Other mistake: In the end roll, Alan Silvestri is credited in the soundtrack as SilveRstri.
Continuity mistake: When Christine and the groom have a look at the battle on the nearby building, in the shot from the front you can see to the left a very excited guy hop from foot to foot with his mouth open. In the angle with the camera behind Christine, the guy is directly next to her, but there were a couple more people between him and the bride.
Continuity mistake: When Strange reveals the presence of the tentacular monster, a person is running across the street behind him with their kid, but they're gone (or rather, several meters behind the original position) in the very next shot.
Continuity mistake: When America says "Find food. Preferably pizza", the passers-by change in the mid-sentence cut.
Continuity mistake: When we first see Wanda with her kids (which turns out to be a dream, but it's also showing a glimpse from another universe, and it's not meant to be 'out of order or unnatural) she tries to tuck one in, and he refuses. Wanda pulls back, but in the next shot she yet has to.
Continuity mistake: At the wedding, Christine tells Stephen that he "deserves it"; she leaves pulling her hand off his tie, but she never put it there in the first place.