I am unable to reproduce this on my test forum. I moved two threads, one read and one unread, to a different forum using inline moderation. They both retained their status.
I run into this as well. Not sure if it is the same in your case but when I am moving threads, I usually change the prefix as well. Thread is then marked as unread.
Got it ... the thread itself isn't marked as unread, that's where I'd gone wrong!! - it's the forum that shows it has unread items!!
Move a thread to a sub-forum (no redirect) - [you'll end up in the sub-forum on the thread you've moved and the sub-forum name will be shown in the navigation breadcrumb] - now ... navigate out of the sub-forum by chosing it's parent (or higher) in the navigation breadcrumb, e.g.;
Forums > Category > Forum > Sub-forum
Now when you look at Forum and Sub-forum they'll both show in bold to indicate they have unread content, even though the content is all read.