Regarding Internet Explorer, I am aware that the configuration page does not work on Internet Explorer 8 and earlier. It does work on Internet Explorer 9 and all other major browsers (tested on Windows 7 Home Premium 64-bit with the 64-bit and fully updated version of IE9 against Akeeba Backup 3.3.1 on Joomla! 1.5.23, 1.6.5 and 1.7.0 running on a live server).
OK, back to your log file. According to this log file, the backup is complete, as noted in these log lines:
DEBUG |110725 16:33:56|Kettenrad :: Just finished
DEBUG |110725 16:33:56|*** Batching of engine steps finished. I will now return control to the caller.
DEBUG |110725 16:33:56|Sleeping for 2975.105047226 msec, using usleep()
DEBUG |110725 16:33:59|Will not save a finished Kettenrad instance
(Kettenrad is the code name of Akeeba Engine 4, the backup engine powering Akeeba Backup 3.x).
If you still get an AJAX error, I'd like to take a look at your site once one.com has finished their upgrades.