My transcript was sent by my undergrad college (in upstate NY) on 5/26 but has yet to be marked as received by AMCAS. Should I be concerned or ask the registrar's office to send them again?
You should be very concerned. It probably means your app will be very late now
@Verbatim Disk One does not need to turn in the "latest" transcript that shows their senior year grades on them. It just has to be an official one. You can always send a full one as an update (I've heard, though I am not sure if it's true or necessary since they don't always look at senior year for GPA related issue, but mostly for trends). So there are students who are graduating this year and may not have their "final" grades released but turned in a transcript from before final grades posted. Thus, your would be "later" than theirs.
Yeah, of course it'll be later, but I don't agree that it'll be "very" late. That's just sdn mentality, and it adds unnecessary scare to the OP. Sending it now will be later, but it won't put you at a significant disadvantage like it would if you submitted your app in August.
You can send updates, but a lot of people don't, and if you have good last quarter grades, having that calculated in your primary is better than an update to every school.