After pasting in 1000 lines, then pasting a 100 line Word doc in that has a lot of formatting, I now see that what seems to be happening is that every so often CE will perform some kind of "background" check and everything I type goes into a buffer until the "background check" is done. This can take several seconds. In a couple of cases, I get the "Warning: unresponsive script" message above.
Anyway, after the background action completes, CE displays everything I typed, but as soon as I type another character or two, it goes into the background thing again.
When the background thing starts, the cursor still is visible. After about 5 to 10 seconds of the background op, the cursor disappears. Typically, is didn't come back for over 20 seconds. However, many times it didn't come back at all until I click back into the document.
I don't think this is a good solution. So far, no problems with the IE implementation but I will check it deeper tonight.