About the -show_err, all you need is this:
"C:\Program Files\Activision\Rome - Total War\RomeTW.exe" -show_err
However, it won't guarantee a message 100% of the time.
Win64 runs some very different things at the lower level, esp. in terms of kernal protection. However, this is not a Win64 issue. It is a codec issue, as Ichbinian implied in his post.
RTW uses movies encoded with MS Media Player 9 codecs. Unfortunately, though the movies are of good quality, these codecs are often in a jumble on people's machines for various reasons. If you want to test them without the game, they are here ...\Rome – Total War\Data\fmv\ .
RTW needs to have the codecs of WMP9 or WMP10 fully installed and functional (e.g., you also need a working sound card and good drivers). Since you have tried the WMP9 codecs on the CD, then you should install WMP10 (purely to get the correct codecs installed an properly registered).
You can download the WMP10 install for XP directly from Microsoft for free:
http://www.microsoft.com/windows/windowsmedia/mp10/default.aspx.If it is still a problem, try ininstalling WMP10, and all other codecs on the machine, including K-lite, Nemo, etc. Then install WMP10 and try playing the videos manually, then in the game.
Good hunting ... PS, I do not run Win64, so if you want to have more of a look at the codec issue, this freeware program might help: GSpot 1.21, http://www.headbands.com/gspot/