Timon, I was a theology student at a Protestant college, and I was also taught that the KJV is not the best translation. It wasn't an acceptable translation for our exegesis papers at all.
That said, I find it to be a wonderful translation, quite close to the Greek in many respects. That said, the OT is based on the Masoretic text, which isn't a bad thing, the Hebrew can be useful, though as you well know it's not traditional in our Church...the LXX takes precedence for us. That said, however, I love it when I hear the KJV used liturgically. It's one of the most beautiful English translations ever produced, surpassing in beauty all of the other Protestant translations like the Geneva Bible (yuck) or even the Bishop's Bible, the Tyndale or Wycliff translations. The D-R is also beautiful, however, as was mentioned above. That would be a tough choice for me, actually, I think.
The problem that I think a lot of folks have with it is exactly what you touched on...people don't readily get it. The English used is several centuries old. It was actually even dated when compared to the vernacular when it was printed in 1611. So, there is an issue of people not really getting the intended meaning, because the meaning of the words have actually changed in English. Problems like this include the use of the word "unicorn", which simply means a horned animal...get over it people! or the phrase of Christ in the Gospels "In my Father's house are many mansions." Of course this doesn't make sense to us...a mansion is a house...a big one! Of course, that's not the meaning of the word mansion as it was used here. The meaning is more along the lines of "dwelling place" without the ritzy connotations the word has acquired for us today. When you understand how the meaning of these words have changed and learn some of the figures of speech being used in the KJV, it becomes a lot easier to read. Sure, it's an added bit of work, but I think the preservation of the older English allows us to closer approximate the Greek in a way that doesn't butcher the Enlgish (ever read the NASB? Ouch!). Modern English just can't do some of the same things it used to!