I finally decided to start moving from the old 2.6x Movabletype to the new 3.1x version. I tried it on an internal blog first. I has one problem after the upgrade : The upgrade somehow overwrote my template files -- I link the templates to a text file on disk so that I can edit them quicker. Stupid me -- I forgot to back those up. Somehow during the upgrade process (from 2.51) overwrote the template files. I still do not understand how that happened.
I really wanted to switch to the new archive file naming convention -- naming the file with the subject text instead of numbers. That is very useful because I can then look at my website access log and can tell immediately what are the popular pages without having to decode the numeric file name. I switched off the "use old archive style" option and rebuilt my site. It created all the new archive pages, and did not delete the old numeric pages. I think that is a good thing. So any external links to the old style page will still work, and hopefully slowly those links get updated.
I then updated this blog to 3.1 also. It went a little smoother, now that I know what to do. I also backed up all my templates before hand. This time my templates were not corrupted. I still did not know what happened.