The problem with Times New Roman is that it's not a web standard font. So any rte is going to have issues with the font itself. It's fine for actual print, but it gets weird with stuff like this. You'd see the same thing in the forum. Which also uses rte as it's edit interface.
Here's an example
See how tiny it made it in comparison? Same font size as Arial. With the serif fonts, I usually go 2 points up, at least. Depending on the font. (This is Book Antigua at 3, Arial is at 2, and so is Times New Roman).
I'll give ya a quick run through with it, different fonts, all at 2 which is the forum default.
Arial
ArialBlack
ArialNarrow
BookAntigua
Century Gothic
Comic Sans MS
Courier New
Franklin Gothic Medium
Garamond
Georgia
Impact
Lucida Console
Lucida Sans Unicode
Microsoft Sans Serif
Palatino Linotype
Tahoma
Times New Roman
Trebuchet MS
Verdana
As you can see, different fonts have different embedded heights and kerning values. That's what makes for the size differences, with the same size selected.
The editor, by the way, is ckeditor, which is the mostly widely used RTE.
@erobey
I think the issue you're having (I looked at the database records), is that almost all of your chapter inserts are bloated html inserts. So, when a chapter is initially opened, it takes one of the core files a bit of time to work through the data and strip out all the garbage the word processor inserted when it exported to html.
It may actually take a couple tries of open the chapter, and save (no edit) to strip out all the extra tags that aren't allowed by the archive to BEGIN with.